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

Jesús González; Mark Grant; Lucile Vandembroucq

doi:10.1090/conm/702/14109

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

Jesús González, Mark Grant, Lucile Vandembroucq

Mathematical Science

University of Minho

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

2 Citations (Scopus)

25 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 language	English
Title of host publication	Topological complexity and related topics
Editors	Mark Grant, Gregory Lupton, Lucile Vandembroucq
Publisher	American Mathematical Society
Pages	133-150
Number of pages	18
Volume	702
ISBN (Electronic)	9781470444051
ISBN (Print)	9781470434366
DOIs	https://doi.org/10.1090/conm/702/14109
Publication status	Published - 2018

Publication series

Name	Contemporary Mathematics
Publisher	American Mathematical Society
ISSN (Print)	1098-3627
ISSN (Electronic)	0271-4132

Keywords

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

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10.1090/conm/702/14109Licence: Unspecified

HOPF INVARIANTS, TOPOLOGICAL COMPLEXITY, AND LS-CATEGORY OF THE COFIBER OF THE DIAGONAL MAP FOR TWO-CELL COMPLEXES
http://www.ams.org/publications/authors/ctp https://creativecommons.org/licenses/by-nc-nd/4.0/
Accepted author manuscript, 258 KBLicence: CC BY-NC-ND

https://arxiv.org/abs/1607.08858Licence: Unspecified

Cite this

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

Hopf invariants, topological complexity, and LS-category of the cofiber of the diagonal map for two-cell complexes. / González, Jesús; Grant, Mark; Vandembroucq, Lucile.
Topological complexity and related topics. ed. / Mark Grant; Gregory Lupton; Lucile Vandembroucq. Vol. 702 American Mathematical Society, 2018. p. 133-150 (Contemporary Mathematics).

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

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N2 - 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

AB - 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

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SN - 9781470434366

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BT - Topological complexity and related topics

A2 - Grant, Mark

A2 - Lupton, Gregory

A2 - Vandembroucq, Lucile

PB - American Mathematical Society

ER -

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

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