We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Relative Topological Complexity and Configuration Spaces.
- Authors
Boehnke, Bryan; Scheirer, Steven; Xue, Shuhang
- Abstract
The topological complexity of a space X, denoted by TC (X) , can be viewed as the minimum number of "continuous rules" needed to describe how to move between any two points in X. Given subspaces Y 1 and Y 2 of X, there is a "relative" version of topological complexity, in which one only considers paths starting at a point y 1 ∈ Y 1 and ending at a point y 2 ∈ Y 2 , but the path from y 1 to y 2 can pass through any point in X. We discuss general results that provide relative analogues of well-known results concerning TC (X) before focusing on configuration spaces. Our primary interest is the case in which configurations must start in some space Y 1 and end in some space Y 2 , but the configurations have an extra degree of motion which allows them to move "above" Y 1 ∪ Y 2 throughout the intermediate stages. We show that in this case, the relative topological complexity is bounded above by TC (Y n) and with certain hypotheses is bounded below by TC (Y) , where Y = Y 1 ∪ Y 2.
- Subjects
TOPOLOGICAL spaces; SUBSPACES (Mathematics)
- Publication
Bulletin of the Iranian Mathematical Society, 2022, Vol 48, Issue 6, p3823
- ISSN
1018-6301
- Publication type
Article
- DOI
10.1007/s41980-022-00723-x