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Topological complexity of wedges and covering maps


Author: Alexander Dranishnikov
Journal: Proc. Amer. Math. Soc. 142 (2014), 4365-4376
MSC (2010): Primary 55M30; Secondary 57N65, 54F45
Published electronically: August 6, 2014
MathSciNet review: 3267004
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Abstract: We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity $ \mathrm {TC}(X)$ and monoidal topological complexity $ \mathrm {TC}^M(X)$. Using these results we provide lower and upper bounds for the topological complexity of the wedge $ X\vee Y$. We use these bounds to give a counterexample to the conjecture asserting that $ \mathrm {TC}(X')\le \mathrm {TC}(X)$ for any covering map $ p : X'\to X$.

Also we discuss a possible reduction of the monoidal topological complexity to the Lusternik-Schnirelmann category.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-2014-12146-0
Received by editor(s): July 31, 2012
Received by editor(s) in revised form: August 11, 2012, August 12, 2012, September 25, 2012, and January 15, 2013
Published electronically: August 6, 2014
Additional Notes: This work was supported by NSF grant DMS-0904278
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2014 American Mathematical Society