Continuation maps for the Morse fundamental group
Abstract
We study properties of the continuation map for the Morse fundamental group [Formula: see text] associated to a Morse–Smale pair [Formula: see text] on a manifold [Formula: see text]. We get a morphism between [Formula: see text] and [Formula: see text] and show that it is functorial. We also define the morphism in the case of Morse data over different manifolds, thanks to the use of grafted trajectories. Finally, given an interpolation function on [Formula: see text] between two Morse functions (used for example to define the continuation map), we study the Morse fundamental group associated to that function and show that it is isomorphic to a relative fundamental group on [Formula: see text].
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometric and Algebraic Topology
Topological and Geometric Data Analysis
Publication details
- Journal / source
- International Journal of Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 37
- Issue
- 09
- Publication date
- 17 April 2026
- Language
- EN