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The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces


Author: Alexander Dranishnikov
Journal: Proc. Amer. Math. Soc. 144 (2016), 4999-5014
MSC (2010): Primary 55M30; Secondary 55S35, 55R05
DOI: https://doi.org/10.1090/proc/13219
Published electronically: June 3, 2016
MathSciNet review: 3544546
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Abstract: We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map of non-orientable surfaces equals three.

Also, we prove that the topological complexity of non-orientable surfaces of genus $ > 4$ is four.


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Additional Information

Alexander Dranishnikov
Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105
Email: dranish@math.ufl.edu

DOI: https://doi.org/10.1090/proc/13219
Received by editor(s): July 6, 2015
Received by editor(s) in revised form: July 14, 2015, August 27, 2015, and January 18, 2016
Published electronically: June 3, 2016
Additional Notes: The author was supported by NSF grant DMS-1304627
Communicated by: Kevin Whyte
Article copyright: © Copyright 2016 American Mathematical Society

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