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Journal of the London Mathematical Society Advance Access published online on June 30, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm105
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© 2008 London Mathematical Society

Bounding volume by systoles of 3-manifolds

Mikhail G. Katz

Department of Mathematics
Bar Ilan University
Ramat Gan 52900
Israel

Yuli B. Rudyak

Department of Mathematics
University of Florida
PO Box 118105
Gainesville
FL 32611-8105
USA
rudyak@math.ufl.edu

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 Z2. 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.

2000 Mathematics Subject Classification 53C23 (primary), 55M30, 57N65 (secondary).

The first author is supported by the Israel Science Foundation (grants 84/03 and 1294/06) and the BSF (grant 2006393). The second author is supported by NSF (grant 0406311).

Received May 18, 2006; revised June 15, 2007;
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