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Bounding volume by systoles of 3‐manifolds
Author(s) -
Katz Mikhail G.,
Rudyak Yuli B.
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm105
Subject(s) - mathematics , bounding overwatch , homotopy , codimension , volume (thermodynamics) , dimension (graph theory) , pure mathematics , combinatorics , computer science , physics , artificial intelligence , quantum mechanics
We prove a new systolic volume lower bound for non‐orientable n ‐manifolds, involving the stable 1‐systole as well as the codimension‐1 systole with coefficients in ℤ 2 . As an application, we prove that Lusternik–Schnirelmann category and systolic category agree for non‐orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category.