Document Type
Article
Publication Date
2010
Publication Title
Algebraic & Geometric Topology
Abstract
In this paper, we study the growth with respect to dimension of quite general homotopy invariants Q applied to the CW skeleta of spaces. This leads to upper estimates analogous to the classical “dimension divided by connectivity” bound for Lusternik–Schnirelmann category. Our estimates apply, in particular, to the Clapp–Puppe theory of A–category. We use cat 1 (X) (which is A–category with A the collection of 1–dimensional CW complexes), to reinterpret in homotopy-theoretical terms some recent work of Dranishnikov on the Lusternik–Schnirelmann category of spaces with fundamental groups of finite cohomological dimension. Our main result is the inequality cat(X)<= dim(BPI1(X))+cat 1(X), which implies and strengthens the main theorem of Dranishnikov [7].
Repository Citation
Oprea, John and Strom, Jeff, "Lusternik–Schnirelmann Category, Complements of Skeleta and A Theorem of Dranishnikov" (2010). Mathematics and Statistics Faculty Publications. 128.
https://engagedscholarship.csuohio.edu/scimath_facpub/128
DOI
10.2140/agt.2010.10.1165
Version
Publisher's PDF
Volume
10
Issue
2
