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arXiv · 1207.7309

On topological complexity and LS-category

Alexander Dranishnikov
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Abstract

We present some results supporting the Iwase-Sakai conjecture about coincidence of the topological complexity $TC(X)$ and monoidal topological complexity $TC^M(X)$. 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 $TC(X')\le TC(X)$ for any covering map $p:X'\to X$. 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.

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Alexander Dranishnikov. 2012-08-12. On topological complexity and LS-category. https://arxiv.org/abs/1207.7309

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