Maps of degree one, relative LS category and higher topological complexities
arXiv:2011.13531
Abstract
In this paper, we introduce relative LS category of a map and study some of its properties. Then we introduce `higher topological complexity' of a map, a homotopy invariant. We give a cohomological lower bound and compare it with previously known `topological complexity' of a map. Moreover, we study the relation between Lusternik-Schnirelmann category and topological complexity of two closed oriented manifolds connected by a degree one map.
19cpages, Example 2.3 and Theorem 5.11 have been corrected, some associated results are added after 5.11, comments are welcome