Morse theory without nondegeneracy

2019/06/26 by Kirwan, Frances, Penington, Geoffrey
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1906.10804

Abstract

We describe an extension of Morse theory to smooth functions on compact Riemannian manifolds, without any nondegeneracy assumptions except that the critical locus must have only finitely many connected components.

Related

• Discrete Morse Theory Is At Least As Perfect As Morse Theory
• The Morse Complex for a Morse Function on a Manifold with Corners
• Smooth functions which are Morse on preimages of values not being local extrema and constructing natural functions of the class on connected sums of manifolds admitting these functions
• Smoothing discrete Morse theory
• Morse theory on manifolds with boundary I. Strong Morse function, cellular structures and algebraic simplification of cellular differential