The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfaces
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- by Alexander Dranishnikov
- Proc. Amer. Math. Soc. 144 (2016), 4999-5014
- DOI: https://doi.org/10.1090/proc/13219
- Published electronically: June 3, 2016
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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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Bibliographic Information
- Alexander Dranishnikov
- Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105
- MR Author ID: 212177
- Email: dranish@math.ufl.edu
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 4999-5014
- MSC (2010): Primary 55M30; Secondary 55S35, 55R05
- DOI: https://doi.org/10.1090/proc/13219
- MathSciNet review: 3544546