Ludwig, Ursula The geometric complex for algebraic curves with cone-like singularities and admissible Morse functions. (English) Zbl 1168.58016 C. R., Math., Acad. Sci. Paris 347, No. 13-14, 801-804 (2009). In the present paper it is given a geometric interpretation of the complex of eigenforms of the Witten Laplace operator corresponding to small eigenvalues. The proof relies on the analysis of an appropriate subcomplex of the complex of unstable cells for the critical points of the admissible Morse function. Reviewer: Vicenţiu D. Rădulescu (Craiova) Cited in 1 Document MSC: 58K45 Singularities of vector fields, topological aspects 32S65 Singularities of holomorphic vector fields and foliations 53A04 Curves in Euclidean and related spaces 58J50 Spectral problems; spectral geometry; scattering theory on manifolds Keywords:geometric complex; algebraic curve; Morse function × Cite Format Result Cite Review PDF Full Text: DOI Numdam References: [1] Bismut, J.-M.; Zhang, W., Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle, Geom. Funct. Anal., 4, 2, 136-212 (1994) · Zbl 0830.58030 [2] Goresky, M.; MacPherson, R., Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 14 (1988), Springer-Verlag: Springer-Verlag Berlin · Zbl 0639.14012 [3] Helffer, B.; Sjöstrand, J., Puits multiples en mécanique semi-classique. IV : Étude du complexe de Witten, Comm. Partial Differential Equations, 10, 3, 245-340 (1985) · Zbl 0597.35024 [4] F. Laudenbach, Appendix: On the Thom-Smale complex, Astérisque 205 (1992); 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, 347, 11-12, 651-654 (2009) · Zbl 1166.32015 [6] Witten, E., Supersymmetry and Morse theory, J. Differential Geom., 17, 4, 661-692 (1982) · Zbl 0499.53056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.