Topological complexity of wedges and covering maps
Alexander Nikolaevich Dranishnikov · Proceedings of the American Mathematical Society · 2014
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.