Publications Repository - Gdańsk University of Technology

Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds M. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions on M that are not necessarily Morse. Finally, we illustrate by an example that this lower bound can indeed be stronger than the lower bound given by the absolute cup-length.

Authors

• Thomas O. Rot,
• dr inż. Maciej Starostka link open in new tab ,
• Nils Waterstraat