A Morse-Bott type complex and the Bismut–Zhang torsion for intersection cohomology
[Un complexe de Morse–Bott et la torsion de Bismut–Zhang en cohomologie d’intersection]
Ludwig, Ursula1
1 University of Münster, Mathematics Münster, Einsteinstrasse 62, 48149 Münster (Germany)
Annales de l'Institut Fourier, Online first, 68 p.

Dans la première partie de cet article on construit, en utilisant la théorie de Morse, pour une pseudovariété stratifiée et une perversité au sens de la théorie de Goresky et MacPherson un complexe cohomologique. Ce complexe calcule la cohomologie d’intersection de la pseudovariété. Dans la deuxième partie on utilise ce complexe ainsi que le Laplacien de Witten pour définir la torsion de Bismut–Zhang, qui, conjecturellement, va servir dans un théorème de Cheeger–Müller pour des pseudovariétés à singularités coniques.

In the first part of this article we establish, for a compact pseudomanifold and a given perversity in the sense of Goresky and MacPherson a Morse theoretical cochain complex, which computes the intersection cohomology of the space. In the second part we use this cochain complex as well as the model Witten Laplacian to define the Bismut–Zhang torsion of a pseudomanifold. Conjecturally the Bismut–Zhang torsion will serve as the “topological” side in a Cheeger–Müller theorem for spaces with iterated conical singularities.

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DOI : 10.5802/aif.3648
Classification : 58J52, 37B30, 55N33
Keywords: Topological and analytic torsion, Morse–Bott complex, intersection cohomology.
Mot clés : Torsion analytic et topologique, complexe de Morse–Bott, cohomologie d’intersection.
Ludwig, Ursula 1

1 University of Münster, Mathematics Münster, Einsteinstrasse 62, 48149 Münster (Germany) 
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Ludwig, Ursula. A Morse-Bott type complex and the Bismut–Zhang torsion for intersection cohomology. Annales de l'Institut Fourier, Online first, 68 p.

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