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Title:

Filling inequalities do not depend on topology

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. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-04

Source:

http://arxiv.org/pdf/0706.2790v3.pdf

http://arxiv.org/pdf/0706.2790v3.pdf Minimize

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text

Language:

en

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Title:

Filling inequalities do not depend on topology

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. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-04

Source:

http://arxiv.org/pdf/0706.2790v2.pdf

http://arxiv.org/pdf/0706.2790v2.pdf Minimize

Document Type:

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. Minimize

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Title:

Topological properties of asymptotic invariants and universal volume bounds

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-04-18

Source:

http://edoc.ub.uni-muenchen.de/8750/1/Brunnbauer_Michael.pdf

http://edoc.ub.uni-muenchen.de/8750/1/Brunnbauer_Michael.pdf Minimize

Document Type:

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. Minimize

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Title:

Homological invariance for asymptotic invariants and systolic inequalities

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. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-04-18

Source:

http://arxiv.org/pdf/math/0702789v1.pdf

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text

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en

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Title:

Filling inequalities do not depend on topology

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. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-04

Source:

http://arxiv.org/pdf/0706.2790v1.pdf

http://arxiv.org/pdf/0706.2790v1.pdf Minimize

Document Type:

text

Language:

en

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Title:

Homological invariance for asymptotic invariants and systolic inequalities

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. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-04-18

Source:

http://arxiv.org/pdf/math/0702789v3.pdf

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text

Language:

en

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Title:

LARGE AND SMALL GROUP HOMOLOGY

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For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large sub-vectorspaces 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 non-large sub-vectorspaces 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). Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-09-24

Source:

http://arxiv.org/pdf/0902.0869v1.pdf

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text

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en

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Title:

Homological invariance for asymptotic invariants and systolic inequalities

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. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-04-18

Source:

http://arxiv.org/pdf/math/0702789v2.pdf

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text

Language:

en

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Title:

On manifolds satisfying stable systolic inequalities

Description:

Abstract. We show that for closed orientable manifolds the k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate cohomology in top-degree. 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 k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate cohomology in top-degree. 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 Eilenberg-MacLane space. Consequently, the stable k-systolic constant is completely determined by the multilinear intersection form on k-dimensional cohomology. 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-26

Source:

http://arxiv.org/pdf/0708.2589v2.pdf

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text

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en

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Title:

On manifolds satisfying stable systolic inequalities

Description:

Abstract. We show that for closed orientable manifolds the k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate real cohomology in top-degree. 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 k-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree k that generate real cohomology in top-degree. 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 Eilenberg-MacLane space. Consequently, the stable k-systolic constant is preserved under degree one maps that induce isomorphisms on k-dimensional homology modulo torsion. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-26

Source:

http://arxiv.org/pdf/0708.2589v1.pdf

http://arxiv.org/pdf/0708.2589v1.pdf Minimize

Document Type:

text

Language:

en

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