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An upper bound for topological complexity. (arXiv:1807.03994v1 [math.AT])
来源于:arXiv
In arXiv:1711.10132 a new approximating invariant
${\mathsf{TC}}^{\mathcal{D}}$ for topological complexity was introduced called
$\mathcal{D}$-topological complexity. In this paper, we explore more fully the
properties of ${\mathsf{TC}}^{\mathcal{D}}$ and the connections between
${\mathsf{TC}}^{\mathcal{D}}$ and invariants of Lusternik-Schnirelmann type. We
also introduce a new $\mathsf{TC}$-type invariant $\widetilde{\mathsf{TC}}$
that can be used to give an upper bound for $\mathsf{TC}$, $$\mathsf{TC}(X)\le
{\mathsf{TC}}^{\mathcal{D}}(X) + \left\lceil \frac{2\dim X
-k}{k+1}\right\rceil,$$ where $X$ is a finite dimensional simplicial complex
with $k$-connected universal cover $\tilde X$. The above inequality is a
refinement of an estimate given by Dranishnikov. 查看全文>>