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UID:6595@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20201217T140000
DTEND;TZID=Europe/Paris:20201217T163000
DTSTAMP:20250118T133252Z
URL:https://www.i2m.univ-amu.fr/evenements/a-morse-bott-type-complex-for-i
 ntersection-homology-and-the-bismut-zhang-torsion/
SUMMARY:Ursula Ludwig (University of Duisburg-Essen\, Germany): A Morse-Bot
 t type complex for intersection homology and the Bismut-Zhang torsion
DESCRIPTION:Ursula Ludwig: The famous Morse-Thom-Smale complex on a smooth 
 compact manifold M associated to a smooth real valued Morse function f is 
 a complex generated by the critical points of the Morse function f and com
 puting the singular (co-)homology of M. An important generalisation of thi
 s complex for smooth Morse-Bott functions is due to Austin and Braam. The 
 Morse-Bott complex of Austin and Braam is generated by the de Rham complex
 es of all critical submanifolds.\nThe aim of this talk is to adapt the con
 struction of Austin and Braam for a stratified pseudomanifold and intersec
 tion cohomology. The main idea is to replace the de Rham complex in the co
 nstruction of Austin and Braam with the complex of liftable intersection f
 orms\, due to Brasselet\, Hector and Saralegi.\nWhile the above constructe
 d "singular'' Morse-Bott type complex may be of some interest in itself\, 
 our main motivation comes from the the comparison theorem of analytic and 
 topological torsion\, aka Cheeger-Müller theorem\, and its generalisation
  to singular spaces\, which in recent years has become a fruitful area of 
 research.\nThe Morse-Bott complex can be used to define a torsion\, which 
 conjecturally could serve as a "topological counterpart'' in a Cheeger-Mü
 ller theorem for wedge singularities.
CATEGORIES:Groupe de travail,Singularités,Virtual event
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