Homotopic distance between maps
E. Mac\'ias-Virg\'os, D. Mosquera-Lois

TL;DR
This paper introduces the homotopic distance between maps, unifying concepts like Lusternik-Schnirelmann category and topological complexity, leading to new insights and simplified proofs of their properties.
Contribution
It defines homotopic distance as a general invariant, encompassing existing invariants, and demonstrates its utility in deriving properties and new results.
Findings
Homotopic distance generalizes Lusternik-Schnirelmann category and topological complexity.
Unified proofs of properties for these invariants.
New results derived from the homotopic distance framework.
Abstract
We show that both Lusternik-Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be proved in a unified way and new results arise.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
