Volume 12, issue 1 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Lusternik–Schnirelmann category and the connectivity of $X$

Nicholas A Scoville

Algebraic & Geometric Topology 12 (2012) 435–448
Abstract

We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces X and Y . This is an invariant based on the connectivity of Ai, where Ai is a space attached in a mapping cone sequence from X to Y . We use the Lusternik–Schnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from X to Y . This theorem is used to prove that for any positive rational number q, there is a space X such that q = clω(X), the connectivity weighted cone-length of X. We compute clω(X) and klω(X) for many spaces and give several examples.

Keywords
Lusternik–Schnirelmann category, categorical sequence, cone length, killing length, Egyptian fractions, mapping cone sequence
Mathematical Subject Classification 2010
Primary: 55M30, 55P05
References
Publication
Received: 25 August 2011
Revised: 8 December 2011
Accepted: 8 December 2011
Published: 20 March 2012
Authors
Nicholas A Scoville
Mathematics and Computer Science
Ursinus College
610 E Main Street
Collegeville PA 19426
USA
http://webpages.ursinus.edu/nscoville/