Activities per year
Abstract
We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow around the critical sets is well-behaved, and the singular space must satisfy a local deformation retract condition. We then show that these conditions are satisfied when the function is the norm-square of a moment map on an affine variety, and that the homotopy equivalence from this theorem is equivariant with respect to the associated Hamiltonian group action. An important special case of these results is that the main theorem of Morse theory holds for the norm square of a moment map on the space of representations of a finite quiver with relations.
Original language | English |
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Pages (from-to) | 4730–4763 |
Number of pages | 34 |
Journal | International Mathematics Research Notices |
Volume | 2019 |
Issue number | 15 |
DOIs | |
Publication status | Published - 18 Nov 2017 |
Bibliographical note
© The Author 2017. Published by Oxford University Press.Profiles
Activities
- 12 Invited talk
-
Morse Theory: Old and new
Wilkin, G. P. D. (Invited speaker)
16 Dec 2024Activity: Talk or presentation › Invited talk
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The Morse complex on singular spaces
Graeme Peter Desmond Wilkin (Invited speaker)
17 Sept 2022Activity: Talk or presentation › Invited talk
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Morse Complex on Singular Spaces
Graeme Peter Desmond Wilkin (Invited speaker)
18 Mar 2022Activity: Talk or presentation › Invited talk
Projects
- 1 Finished
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Morse-Kirwan theory on singular spaces
1/09/14 → 31/01/18
Project: Other project › Project from former institution