2021
DOI: 10.1093/qmath/haaa064
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Morse Theory without Non-Degeneracy

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

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Cited by 4 publications
(2 citation statements)
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References 70 publications
(85 reference statements)
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“…Index pairs for isolated critical points of smooth functions have been thoroughly explored by Gromoll and Meyer [13]; the work of Chang and Ghoussoub [3] provides a convenient dictionary between Conley's index pairs and a generalised version of these Gromoll-Meyer pairs. Also close in spirit and generality to our (N , N − ) are the systems of Morse neighbourhoods around arbitrary isolated critical sets in the recent work of Kirwan and Penington [16].…”
Section: Introductionsupporting
confidence: 53%
“…Index pairs for isolated critical points of smooth functions have been thoroughly explored by Gromoll and Meyer [13]; the work of Chang and Ghoussoub [3] provides a convenient dictionary between Conley's index pairs and a generalised version of these Gromoll-Meyer pairs. Also close in spirit and generality to our (N , N − ) are the systems of Morse neighbourhoods around arbitrary isolated critical sets in the recent work of Kirwan and Penington [16].…”
Section: Introductionsupporting
confidence: 53%
“…Isomorphisms of quiver representations can be used to characterise, for example, the Jordan normal form of matrices and the Kronecker normal form of matrix pencils. They also play an important role in various other fields, including the study of associative algebras [3], Gromov-Witten invariants [22], representations of Kac-Moody algebras [39], moduli stacks [48], Morse theory [35], persistent homology [41], and perverse sheaves [19], among others.…”
Section: Introductionmentioning
confidence: 99%