Cross-sections of Milnor fibrations and Motion planning

Abstract

Consider a fibration \[p:E\to S^{p-1}\] with fiber $F$. We have the following natural question: Under what conditions does this fibration admit a cross-section? Our purpose is to discuss this problem when the fibration $p$ is the Milnor fibration $f_{\mid }:f^{-1}(S_{\delta }^{p-1})\cap D_{\epsilon }^n\to S_{\delta }^{p-1}$ 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.

13 pages, 1 figure. Comments are welcome!

References in corpus (1)

• On the topology of the Milnor fibration of a hyperplane arrangement