截面范畴的Hopf不变量及其在拓扑机器人学中的应用
代数拓扑
2017-07-18 v4
摘要
我们在截面范畴的框架下发展了广义Hopf不变量理论。特别地，我们展示了如何将纤维积的Hopf不变量识别为因子Hopf不变量的shuffle join。我们的结果应用于2-胞腔复形的Farber拓扑复杂度的研究，以及构造一个反例，该反例针对拓扑复杂度的Ganea猜想的类似物（关于Lusternik-Schnirelmann范畴）。
引用
@article{arxiv.1405.6891,
title = {Hopf Invariants for sectional category with applications to topological robotics},
author = {Jesús González and Mark Grant and Lucile Vandembroucq},
journal= {arXiv preprint arXiv:1405.6891},
year = {2017}
}
备注
v4: 39 pages, incorporating comments from a referee. v3: 38 pages. Improved exposition and strengthened our results on TC of 2-cell complexes. v2: 36 pages. Completely re-written, with a new co-author and new title. We now calculate TC of many 2-cell complexes in the metastable range, and exhibit a counter-example to the TC analogue of Ganea's conjecture