Relative systoles of relative-essential 2-complexes

Karin Usadi Katz; Mikhail G. Katz; Stéphane Sabourau; Steven Shnider; Shmuel Weinberger

doi:https://doi.org/10.2140/agt.2011.11.197

Relative systoles of relative-essential 2-complexes

Karin Usadi Katz, Mikhail G. Katz, Stéphane Sabourau, Steven Shnider, Shmuel Weinberger

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a systolic inequality for a Π-relative systole of a Π-essential 2-complex X, where Π: π₁→ G is a homomorphism to a finitely presented group G. Thus, we show that universally for any Π-essential Riemannian 2-complex X, and any G, the following inequality is satisfied: sys(X, Π)² ≤8Area(X). Combining our results with a method of L Guth, we obtain new quantitative results for certain 3-manifolds: in particular for the Poincaré homology sphere Σ, we have sys(Σ)³ ≤ 24Vol(Σ).

Original language	English
Pages (from-to)	197-217
Number of pages	21
Journal	Algebraic and Geometric Topology
Volume	11
Issue number	1
DOIs	https://doi.org/10.2140/agt.2011.11.197
State	Published - 2011

All Science Journal Classification (ASJC) codes

Geometry and Topology

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title = "Relative systoles of relative-essential 2-complexes",

abstract = "We prove a systolic inequality for a Π-relative systole of a Π-essential 2-complex X, where Π: π1→ G is a homomorphism to a finitely presented group G. Thus, we show that universally for any Π-essential Riemannian 2-complex X, and any G, the following inequality is satisfied: sys(X, Π)2 ≤8Area(X). Combining our results with a method of L Guth, we obtain new quantitative results for certain 3-manifolds: in particular for the Poincar{\'e} homology sphere Σ, we have sys(Σ)3 ≤ 24Vol(Σ).",

author = "Katz, {Karin Usadi} and Katz, {Mikhail G.} and St{\'e}phane Sabourau and Steven Shnider and Shmuel Weinberger",

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AU - Katz, Karin Usadi

AU - Katz, Mikhail G.

AU - Sabourau, Stéphane

AU - Shnider, Steven

AU - Weinberger, Shmuel

N1 - cited By 5

PY - 2011

Y1 - 2011

N2 - We prove a systolic inequality for a Π-relative systole of a Π-essential 2-complex X, where Π: π1→ G is a homomorphism to a finitely presented group G. Thus, we show that universally for any Π-essential Riemannian 2-complex X, and any G, the following inequality is satisfied: sys(X, Π)2 ≤8Area(X). Combining our results with a method of L Guth, we obtain new quantitative results for certain 3-manifolds: in particular for the Poincaré homology sphere Σ, we have sys(Σ)3 ≤ 24Vol(Σ).

AB - We prove a systolic inequality for a Π-relative systole of a Π-essential 2-complex X, where Π: π1→ G is a homomorphism to a finitely presented group G. Thus, we show that universally for any Π-essential Riemannian 2-complex X, and any G, the following inequality is satisfied: sys(X, Π)2 ≤8Area(X). Combining our results with a method of L Guth, we obtain new quantitative results for certain 3-manifolds: in particular for the Poincaré homology sphere Σ, we have sys(Σ)3 ≤ 24Vol(Σ).

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U2 - https://doi.org/10.2140/agt.2011.11.197

DO - https://doi.org/10.2140/agt.2011.11.197

M3 - مقالة

SN - 1472-2747

VL - 11

SP - 197

EP - 217

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

ER -

Relative systoles of relative-essential 2-complexes

Abstract

All Science Journal Classification (ASJC) codes

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