A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation

Ursula Ludwig[1]

  • [1] Universität Freiburg Mathematisches Institut Eckerstrasse 1 79104 Freiburg (Allemagne)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 5, page 1749-1777
  • ISSN: 0373-0956

Abstract

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The Witten deformation is an analytic method proposed by Witten which, given a Morse function f : M → R on a smooth compact manifold M , allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities and a certain class of functions called admissible Morse functions. The perturbation arguments needed to understand the Witten deformation on the curve with its metric induced from the Fubini-Study metric of the ambient projective space and for any stratified Morse function are presented here.

How to cite

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Ludwig, Ursula. "A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation." Annales de l’institut Fourier 61.5 (2011): 1749-1777. <http://eudml.org/doc/219758>.

@article{Ludwig2011,
abstract = {The Witten deformation is an analytic method proposed by Witten which, given a Morse function $f : M \rightarrow \bf R$ on a smooth compact manifold $M$, allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities and a certain class of functions called admissible Morse functions. The perturbation arguments needed to understand the Witten deformation on the curve with its metric induced from the Fubini-Study metric of the ambient projective space and for any stratified Morse function are presented here.},
affiliation = {Universität Freiburg Mathematisches Institut Eckerstrasse 1 79104 Freiburg (Allemagne)},
author = {Ludwig, Ursula},
journal = {Annales de l’institut Fourier},
keywords = {Morse theory; Witten deformation; Cone-like Singularities; cone-like singularities},
language = {eng},
number = {5},
pages = {1749-1777},
publisher = {Association des Annales de l’institut Fourier},
title = {A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation},
url = {http://eudml.org/doc/219758},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ludwig, Ursula
TI - A proof of the stratified Morse inequalities for singular complex algebraic curves using the Witten deformation
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 5
SP - 1749
EP - 1777
AB - The Witten deformation is an analytic method proposed by Witten which, given a Morse function $f : M \rightarrow \bf R$ on a smooth compact manifold $M$, allows to prove the Morse inequalities. The aim of this article is to generalise the Witten deformation to stratified Morse functions (in the sense of stratified Morse theory as developed by Goresky and MacPherson) on a singular complex algebraic curve. In a previous article the author developed the Witten deformation for the model of an algebraic curve with cone-like singularities and a certain class of functions called admissible Morse functions. The perturbation arguments needed to understand the Witten deformation on the curve with its metric induced from the Fubini-Study metric of the ambient projective space and for any stratified Morse function are presented here.
LA - eng
KW - Morse theory; Witten deformation; Cone-like Singularities; cone-like singularities
UR - http://eudml.org/doc/219758
ER -

References

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