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F-MAT-Naturvitenskap, matematikk

Morse theory and diffeomorhism

Awarded: NOK 1.6 mill.

Morse theory is built on the idea that the singularity structure of smooth functions on a differntiable manifold may give rise to a cell structure on the manifold, and hence will determine its homotopy type. This often makes sense also for infinite dimens ional manifolds, and the objective of this project is to try to carry this out for diffeomorphism groups of compact, smooth manifolds, or possibly for spaces of loops on these groups. The main problem will be to find and investigate suitable "energy" func tions built up using the geometric structure on the manifold. This should give rise to new invariants and new information on the homotopy groups of these diffeomorphism groups. In the end, it will be of great interest to compare these results to calculati ons using algebraic K-Theory of spaces, to help clarify the relationship between diffeomorphism groups and this theory.

Funding scheme:

F-MAT-Naturvitenskap, matematikk

Thematic Areas and Topics

No thematic area or topic related to the project