Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes

Jesús González, Mark Grant, Lucile Vandembroucq

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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23 Downloads (Pure)

Abstract

Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the Lusternik-Schnirelmann category (${\rm cat}$) of $C_X$ in the (almost stable) range $q\leq2p-1$. In addition, the equality ${\rm TC}(X)={\rm cat}(C_X)$ is proved in the (strict) metastable range $2p-1
Original languageEnglish
Title of host publicationTopological complexity and related topics
EditorsMark Grant, Gregory Lupton, Lucile Vandembroucq
PublisherAmerican Mathematical Society
Pages133-150
Number of pages18
Volume702
ISBN (Electronic)9781470444051
ISBN (Print)9781470434366
DOIs
Publication statusPublished - 2018

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
ISSN (Print)1098-3627
ISSN (Electronic)0271-4132

Keywords

  • math.AT
  • 55M30, 55Q25, 55S35, 55S36, 68T40, 70B15

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    González, J., Grant, M., & Vandembroucq, L. (2018). Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes. In M. Grant, G. Lupton, & L. Vandembroucq (Eds.), Topological complexity and related topics (Vol. 702, pp. 133-150). (Contemporary Mathematics). American Mathematical Society. https://doi.org/10.1090/conm/702/14109