no. 3
Differential geometry
An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities
[Une extension d'un résultat de Cheeger et Müller pour un espace à singularités coniques isolées]

Présenté par : the Editorial Board

Ludwig, Ursula1
1 Universität Duisburg-Essen, Fakultät für Mathematik, 45117 Essen, Germany
Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 327-332.

Le but de cette note est d'établir un théorème de Cheeger–Müller pour un espace a singularités coniques isolées en généralisant la preuve de Bismut et Zhang. Les outils utilisés dans la preuve sont les techniques d'indice local et la déformation de Witten.

The aim of this note is to extend a theorem by Cheeger and Müller to spaces with isolated conical singularities by generalising the proof of Bismut and Zhang to the singular setting. The main tools in this approach are the Witten deformation and local index techniques.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.01.012
Ludwig, Ursula 1

1 Universität Duisburg-Essen, Fakultät für Mathematik, 45117 Essen, Germany 
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Ludwig, Ursula. An extension of a theorem by Cheeger and Müller to spaces with isolated conical singularities. Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 327-332. doi : 10.1016/j.crma.2018.01.012. http://archive.numdam.org/articles/10.1016/j.crma.2018.01.012/

[1] Bismut, J.-M.; Zhang, W. An Extension of a Theorem by Cheeger and Müller, Astérisque, vol. 205, Société mathématique de France, Paris, 1992 (With an appendix by François Laudenbach)

[2] Cheeger, J. Analytic torsion and the heat equation, Ann. of Math. (2), Volume 109 (1979), pp. 259-322

[3] Cheeger, J. On the Hodge theory of Riemannian pseudomanifolds, Geometry of the Laplace Operator, Proc. Sympos. Pure Math., vol. XXXVI, American Mathematical Society, Providence, RI, USA, 1980, pp. 91-146

[4] Cheeger, J. Spectral geometry of singular Riemannian spaces, J. Differ. Geom., Volume 18 (1983) no. 4, pp. 575-657

[5] Dar, A. Intersection R-torsion and analytic torsion for pseudomanifolds, Math. Z., Volume 194 (1987), pp. 193-216

[6] Goresky, M.; MacPherson, R. Intersection homology II, Invent. Math., Volume 72 (1983), pp. 77-129

[7] Hartmann, L.; Spreafico, M. On the Cheeger–Müller theorem for an even-dimensional cone, St. Petersburg Math. J., Volume 27 (2016) no. 1, pp. 137-154

[8] Lesch, M. A gluing formula for the analytic torsion on singular spaces, Anal. PDE, Volume 6 (2013) no. 1, pp. 221-256

[9] Ludwig, U. Comparison between two complexes on a singular space, J. Reine Angew. Math., Volume 724 (2017), pp. 1-52

[10] Ludwig, U. A complex in Morse theory computing intersection homology, Ann. Inst. Fourier, Volume 67 (2017) no. 1, pp. 197-236

[11] Ludwig, U. An index theorem for the intersection Euler characteristic of the infinite cone, C. R. Acad. Sci. Paris, Ser. I, Volume 355 (2017) no. 1, pp. 94-98

[12] Müller, W. Analytic torsion and R-torsion of Riemannian manifolds, Adv. Math., Volume 28 (1978), pp. 233-305

[13] Müller, W.; Vertman, B. The metric anomaly of analytic torsion on manifolds with conical singularities, Commun. Partial Differ. Equ., Volume 39 (2014) no. 1, pp. 146-191

[14] Ray, D.B.; Singer, I.M. R-torsion and the Laplacian on Riemannian manifolds, Adv. Math., Volume 7 (1971), pp. 145-210

[15] Smale, S. On gradient dynamical systems, Ann. of Math. (2), Volume 74 (1961), pp. 199-206

[16] Vertman, B. Analytic torsion of a bounded generalized cone, Commun. Math. Phys., Volume 290 (2009) no. 3, pp. 813-860

[17] Vishik, S.M. Generalized Ray–Singer conjecture. I: a manifold with a smooth boundary, Commun. Math. Phys., Volume 167 (1995) no. 1, pp. 1-102

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