Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 1 (2012), 435-448.
Lusternik–Schnirelmann category and the connectivity of $X$
We define and study a homotopy invariant called the connectivity weight to compute the weighted length between spaces and . This is an invariant based on the connectivity of , where is a space attached in a mapping cone sequence from to . We use the Lusternik–Schnirelmann category to prove a theorem concerning the connectivity of all spaces attached in any decomposition from to . This theorem is used to prove that for any positive rational number , there is a space such that , the connectivity weighted cone-length of . We compute and for many spaces and give several examples.
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 435-448.
Received: 25 August 2011
Revised: 8 December 2011
Accepted: 8 December 2011
First available in Project Euclid: 19 December 2017
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Scoville, Nicholas A. Lusternik–Schnirelmann category and the connectivity of $X$. Algebr. Geom. Topol. 12 (2012), no. 1, 435--448. doi:10.2140/agt.2012.12.435. https://projecteuclid.org/euclid.agt/1513715345