Differential Geometry
The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 801-804.

In a previous Note the author gave a generalisation of Witten's proof of the Morse inequalities to the model of a singular complex algebraic curve X and a stratified Morse function f. In this Note a geometric interpretation of the complex of eigenforms of the Witten Laplacian corresponding to small eigenvalues is provided in terms of an appropriate subcomplex of the complex of unstable cells of critical points of f.

Dans une Note précédente, l'auteur a donné une généralisation de la preuve de Witten des inegalités de Morse pour le cas modèle d'une courbe algébrique complexe singulière et d'une fonction de Morse stratifiée. Le but de cette Note est de donner une interprétation géométrique du complexe des formes propres du Laplacien de Witten pour de petites valeurs propres à l'aide d'un sous-complexe approprié du complexe des cellules instables.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.028
Ludwig, Ursula 1

1 Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany
@article{CRMATH_2009__347_13-14_801_0,
     author = {Ludwig, Ursula},
     title = {The geometric complex for algebraic curves with cone-like singularities and admissible {Morse} functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {801--804},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     year = {2009},
     doi = {10.1016/j.crma.2009.03.028},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.028/}
}
TY  - JOUR
AU  - Ludwig, Ursula
TI  - The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 801
EP  - 804
VL  - 347
IS  - 13-14
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.03.028/
DO  - 10.1016/j.crma.2009.03.028
LA  - en
ID  - CRMATH_2009__347_13-14_801_0
ER  - 
%0 Journal Article
%A Ludwig, Ursula
%T The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions
%J Comptes Rendus. Mathématique
%D 2009
%P 801-804
%V 347
%N 13-14
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.03.028/
%R 10.1016/j.crma.2009.03.028
%G en
%F CRMATH_2009__347_13-14_801_0
Ludwig, Ursula. The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 801-804. doi : 10.1016/j.crma.2009.03.028. http://www.numdam.org/articles/10.1016/j.crma.2009.03.028/

[1] Bismut, J.-M.; Zhang, W. Milnor and Ray–Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal., Volume 4 (1994) no. 2, pp. 136-212

[2] Goresky, M.; MacPherson, R. Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Results in Mathematics and Related Areas (3), vol. 14, Springer-Verlag, Berlin, 1988

[3] Helffer, B.; Sjöstrand, J. Puits multiples en mécanique semi-classique. IV : Étude du complexe de Witten, Comm. Partial Differential Equations, Volume 10 (1985) no. 3, pp. 245-340

[4] F. Laudenbach, Appendix: On the Thom–Smale complex, Astérisque 205 (1992)

[5] Ludwig, U. The Witten complex for algebraic curves with cone-like singularities, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009) no. 11–12, pp. 651-654

[6] Witten, E. Supersymmetry and Morse theory, J. Differential Geom., Volume 17 (1982) no. 4, pp. 661-692

Cited by Sources: