Crosssections of Milnor fibrations and Motion planning
Abstract
Consider a fibration \[p:E\to S^{p1}\] with fiber $F$. We have the following natural question: Under what conditions does this fibration admit a crosssection? Our purpose is to discuss this problem when the fibration $p$ is the Milnor fibration $f_{\mid}:f^{1}(S^{p1}_{\delta})\cap D^{n}_{\epsilon}\to S^{p1}_{\delta}$ with Milnor fiber $F_f$ and the Milnor fibration of arrangements $Q:\mathcal{M}(\mathcal{A})\to \mathbb{C}^\ast$ with fiber $F=F(\mathcal{A})$. Furthermore, we use our results to study the tasking planning problem for the Milnor fibration as a work map and we give the tasking algorithms.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 DOI:
 10.48550/arXiv.1910.00157
 arXiv:
 arXiv:1910.00157
 Bibcode:
 2019arXiv191000157Z
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Algebraic Geometry
 EPrint:
 13 pages, 1 figure. Comments are welcome!