Geodesic
Lusternik–Schnirelmann category and the connectivity of X
Scoville, Nicholas A1
1Mathematics and Computer Science, Ursinus College, 610 E Main Street, Collegeville PA 19426, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 435-448
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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.

DOI : 10.2140/agt.2012.12.435
Classification : 55M30, 55P05
Keywords: Lusternik–Schnirelmann category, categorical sequence, cone length, killing length, Egyptian fractions, mapping cone sequence

Scoville, Nicholas A  1

1 Mathematics and Computer Science, Ursinus College, 610 E Main Street, Collegeville PA 19426, USA 
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Scoville, Nicholas A. Lusternik–Schnirelmann category and the connectivity of X. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 435-448. doi: 10.2140/agt.2012.12.435

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