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1.
Topological properties of asymptotic invariants and universal volume bounds
Open Access
Title:
Topological properties of asymptotic invariants and universal volume bounds
Author:
Michael Brunnbauer
Michael Brunnbauer
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130418
Source:
http://edoc.ub.unimuenchen.de/8750/1/
Brunnbauer
_Michael.pdf
http://edoc.ub.unimuenchen.de/8750/1/
Brunnbauer
_Michael.pdf
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text
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en
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.193.3916
http://edoc.ub.unimuenchen.de/8750/1/Brunnbauer_Michael.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.193.3916
http://edoc.ub.unimuenchen.de/8750/1/Brunnbauer_Michael.pdf
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2.
LARGE AND SMALL GROUP HOMOLOGY
Open Access
Title:
LARGE AND SMALL GROUP HOMOLOGY
Author:
Michael Brunnbauer
;
Bernhard Hanke
Michael Brunnbauer
;
Bernhard Hanke
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For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct nonlarge subvectorspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds depend only on the image of th...
For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct nonlarge subvectorspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds depend only on the image of their fundamental classes under the classifying map. This is applied to construct, amongst others, examples of essential manifolds whose universal covers are not hyperspherical, thus answering a question of Gromov (1986).
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Year of Publication:
20140924
Source:
http://arxiv.org/pdf/0902.0869v1.pdf
http://arxiv.org/pdf/0902.0869v1.pdf
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en
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.242
http://arxiv.org/pdf/0902.0869v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.242
http://arxiv.org/pdf/0902.0869v1.pdf
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3.
Filling inequalities do not depend on topology
Open Access
Title:
Filling inequalities do not depend on topology
Author:
Michael Brunnbauer
Michael Brunnbauer
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Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contr...
Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold. 1.
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Year of Publication:
20121204
Source:
http://arxiv.org/pdf/0706.2790v3.pdf
http://arxiv.org/pdf/0706.2790v3.pdf
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.3738
http://arxiv.org/pdf/0706.2790v3.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.3738
http://arxiv.org/pdf/0706.2790v3.pdf
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4.
Filling inequalities do not depend on topology
Open Access
Title:
Filling inequalities do not depend on topology
Author:
Michael Brunnbauer
Michael Brunnbauer
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Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contr...
Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold. 1.
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Year of Publication:
20121204
Source:
http://arxiv.org/pdf/0706.2790v1.pdf
http://arxiv.org/pdf/0706.2790v1.pdf
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.6939
http://arxiv.org/pdf/0706.2790v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.250.6939
http://arxiv.org/pdf/0706.2790v1.pdf
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5.
Filling inequalities do not depend on topology
Open Access
Title:
Filling inequalities do not depend on topology
Author:
Michael Brunnbauer
Michael Brunnbauer
Minimize authors
Description:
Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contr...
Abstract. Gromov’s universal filling inequalities relate the filling radius and the filling volume of a Riemannian manifold to its volume. The main result of the present article is that in dimensions at least three the optimal constants in the filling inequalities depend only on dimension and orientability, not on the manifold itself. This contrasts with the analogous situation for the optimal systolic inequality, which does depend on the manifold. 1.
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Year of Publication:
20121204
Source:
http://arxiv.org/pdf/0706.2790v2.pdf
http://arxiv.org/pdf/0706.2790v2.pdf
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text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.1999
http://arxiv.org/pdf/0706.2790v2.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.251.1999
http://arxiv.org/pdf/0706.2790v2.pdf
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6.
Homological invariance for asymptotic invariants and systolic inequalities
Open Access
Title:
Homological invariance for asymptotic invariants and systolic inequalities
Author:
Michael Brunnbauer
Michael Brunnbauer
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Description:
We show that the systolic constant, the minimal entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental groups of order two (modulo the value on the real projective space) and der...
We show that the systolic constant, the minimal entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental groups of order two (modulo the value on the real projective space) and derive an inequality between the minimal entropy and the systolic constant.
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130418
Source:
http://arxiv.org/pdf/math/0702789v1.pdf
http://arxiv.org/pdf/math/0702789v1.pdf
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text
Language:
en
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Metadata may be used without restrictions as long as the oai identifier remains attached to it.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.8053
http://arxiv.org/pdf/math/0702789v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.8053
http://arxiv.org/pdf/math/0702789v1.pdf
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7.
Homological invariance for asymptotic invariants and systolic inequalities
Open Access
Title:
Homological invariance for asymptotic invariants and systolic inequalities
Author:
Michael Brunnbauer
Michael Brunnbauer
Minimize authors
Description:
We show that the systolic constant, the minimal volume entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value for the real projective space) ...
We show that the systolic constant, the minimal volume entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value for the real projective space) and derive an inequality between the minimal volume entropy and the systolic constant.
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130418
Source:
http://arxiv.org/pdf/math/0702789v3.pdf
http://arxiv.org/pdf/math/0702789v3.pdf
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text
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.1965
http://arxiv.org/pdf/math/0702789v3.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.1965
http://arxiv.org/pdf/math/0702789v3.pdf
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8.
On manifolds satisfying stable systolic inequalities
Open Access
Title:
On manifolds satisfying stable systolic inequalities
Author:
Michael Brunnbauer
Michael Brunnbauer
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Abstract. We show that for closed orientable manifolds the kdimensional stable systole admits a metricindependent volume bound if and only if there are cohomology classes of degree k that generate real cohomology in topdegree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at...
Abstract. We show that for closed orientable manifolds the kdimensional stable systole admits a metricindependent volume bound if and only if there are cohomology classes of degree k that generate real cohomology in topdegree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at least two. Additionally, we prove that the stable systolic constant depends only on the image of the fundamental class in a suitable EilenbergMacLane space. Consequently, the stable ksystolic constant is preserved under degree one maps that induce isomorphisms on kdimensional homology modulo torsion. 1.
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Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0708.2589v1.pdf
http://arxiv.org/pdf/0708.2589v1.pdf
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.1965
http://arxiv.org/pdf/0708.2589v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.1965
http://arxiv.org/pdf/0708.2589v1.pdf
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9.
On manifolds satisfying stable systolic inequalities
Open Access
Title:
On manifolds satisfying stable systolic inequalities
Author:
Michael Brunnbauer
Michael Brunnbauer
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Description:
Abstract. We show that for closed orientable manifolds the kdimensional stable systole admits a metricindependent volume bound if and only if there are cohomology classes of degree k that generate cohomology in topdegree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at leas...
Abstract. We show that for closed orientable manifolds the kdimensional stable systole admits a metricindependent volume bound if and only if there are cohomology classes of degree k that generate cohomology in topdegree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles of dimension at least two. Additionally, we prove that the stable systolic constant depends only on the image of the fundamental class in a suitable EilenbergMacLane space. Consequently, the stable ksystolic constant is completely determined by the multilinear intersection form on kdimensional cohomology. 1.
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Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0708.2589v2.pdf
http://arxiv.org/pdf/0708.2589v2.pdf
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text
Language:
en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.9917
http://arxiv.org/pdf/0708.2589v2.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.9917
http://arxiv.org/pdf/0708.2589v2.pdf
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10.
Homological invariance for asymptotic invariants and systolic inequalities
Open Access
Title:
Homological invariance for asymptotic invariants and systolic inequalities
Author:
Michael Brunnbauer
Michael Brunnbauer
Minimize authors
Description:
We show that the systolic constant, the minimal volume entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value for the real projective space) ...
We show that the systolic constant, the minimal volume entropy, and the spherical volume of a manifold depend only on the image of the fundamental class under the classifying map of the universal covering. Moreover, we compute the systolic constant of manifolds with fundamental group of order two (modulo the value for the real projective space) and derive an inequality between the minimal volume entropy and the systolic constant.
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The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20130418
Source:
http://arxiv.org/pdf/math/0702789v2.pdf
http://arxiv.org/pdf/math/0702789v2.pdf
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en
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.6879
http://arxiv.org/pdf/math/0702789v2.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.240.6879
http://arxiv.org/pdf/math/0702789v2.pdf
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