Degenerate Morse theory and quivers

26 November 2019
Frances Kirwan

This talk is an update on joint work with Geoff Penington on extending Morse theory to smooth functions on compact manifolds with very mild nondegeneracy assumptions. The only requirement is that the critical locus should have just finitely many connected components. To such a function we associate a quiver with vertices labelled by the connected components of the critical locus. The analogue of the Morse–Witten complex in this situation is a spectral sequence of multicomplexes supported on this quiver which abuts to the homology of the manifold.

  • Algebraic Geometry Seminar