Topological complexity of $H$-spaces
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- by Gregory Lupton and Jérôme Scherer PDF
- Proc. Amer. Math. Soc. 141 (2013), 1827-1838 Request permission
Abstract:
Let $X$ be a (not-necessarily homotopy-associative) $H$-space. We show that $\mathrm {TC}_{n+1}(X) = \mathrm {cat}(X^n)$, for $n \geq 1$, where $\mathrm {TC}_{n+1}(-)$ denotes the so-called higher topological complexity introduced by Rudyak, and $\mathrm {cat}(-)$ denotes the Lusternik-Schnirelmann category. We also generalize this equality to an inequality, which gives an upper bound for $\mathrm {TC}_{n+1}(X)$, in the setting of a space $Y$ acting on $X$.References
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Additional Information
- Gregory Lupton
- Affiliation: Department of Mathematics, Cleveland State University, Cleveland, Ohio 44115
- MR Author ID: 259990
- Email: G.Lupton@csuohio.edu
- Jérôme Scherer
- Affiliation: SB Mathgeom, Ma B3 455, Station 8, EPFL, CH-1015 Lausanne, Switzerland
- Email: jerome.scherer@epfl.ch
- Received by editor(s): June 16, 2011
- Received by editor(s) in revised form: September 2, 2011
- Published electronically: October 23, 2012
- Additional Notes: The first author acknowledges the hospitality and support of EPFL and the support of the Cleveland State University FRD grant program.
The second author is partially supported by FEDER/MEC grant MTM2010-20692. Both authors acknowledge the support of the Swiss National Science Foundation (project IZK0Z2_133237). - Communicated by: Brooke Shipley
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1827-1838
- MSC (2010): Primary 55M30, 55S40, 57T99, 70Q05
- DOI: https://doi.org/10.1090/S0002-9939-2012-11454-6
- MathSciNet review: 3020869