On topological complexity and LS-category

Abstract

We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity $TC(X)$ and monoidal topological complexity $T{C}^M(X)$. 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 $TC(X^{\prime })\le TC(X)$ for any covering map $p:X^{\prime }\to X$. We discuss a possible reduction of the monoidal topological complexity to the LS-category. Also we apply the LS-category to give a short proof of the Arnold-Kuiper theorem.

15 pages

Cited by in corpus (1)

• Whitehead and Ganea constructions for fibrewise sectional category