Lusternik-Schnirelmann category and based topological complexities of motion planning

Yongheng Zhang

Lusternik-Schnirelmann category and based topological complexities of motion planning

Algebraic Topology 2015-08-20 v2

Authors: Yongheng Zhang

Abstract

Farber and Rudyak introduced topological complexity $\mathbf{TC}(X)$ of motion planning and its higher analogs $\mathbf{TC}_n(X)$ to measure the complexity of assigning paths to point tuples. Motivated by motion planning where a robotic system starts at the home configuration and possibly comes back after passing through a list of locations, we define three other classes of topological complexities $\mathbf{LTC}_n(X)$ , $\mathbf{ltc}_n(X)$ and $\mathbf{tc}_n(X)$ . We will compare these notions and compute the latter for some familiar classes of spaces.

Keywords

Lusternik-Schnirelmann category topological complexity motion planning based topological complexity path assignment

Cite

@article{arxiv.1508.04209,
  title  = {Lusternik-Schnirelmann category and based topological complexities of motion planning},
  author = {Yongheng Zhang},
  journal= {arXiv preprint arXiv:1508.04209},
  year   = {2015}
}

Comments

7 pages; comments added: LTC_2(X) was introduced earlier by My Ismail Mamouni and Derfoufi Younes and they concluded that LTC_2(X)=TC(X)

Lusternik-Schnirelmann category and based topological complexities of motion planning

Abstract

Keywords

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