Topological complexity of wedges and covering maps

Dranishnikov, Alexander

doi:10.1090/S0002-9939-2014-12146-0

Topological complexity of wedges and covering maps
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by Alexander Dranishnikov

Proc. Amer. Math. Soc. 142 (2014), 4365-4376

DOI: https://doi.org/10.1090/S0002-9939-2014-12146-0

Published electronically: August 6, 2014

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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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