TY - JOUR
T1 - Relative systoles of relative-essential 2-complexes
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).
UR - http://www.scopus.com/inward/record.url?scp=79952927274&partnerID=8YFLogxK
U2 - 10.2140/agt.2011.11.197
DO - 10.2140/agt.2011.11.197
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SN - 1472-2747
VL - 11
SP - 197
EP - 217
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 1
ER -