Index theory via deformation groupoids - Thèses et HDR de l'INSA Toulouse
Hdr Année : 2023

Index theory via deformation groupoids

Résumé

The goal of this memoir is to present and describe a handful of different index theorems and index related problems associated to different geometric situations. The common point of all the results presented here is the use of groupoids and more particularly deformation groupoids, and the use of algebraic topology tools (like K-theory, Cyclic (co)homology and others) to state and proof some analytic index problems. As I will try to settle down, there are many different situations that can be unified and treated in a relatively common setting by adopting the groupoid perspective. But beyond the interest of getting an unified treatment for several problems, I will show how groupoids and deformation groupoids can be used to get explicit original answers to complex problems in index theory.
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Dates et versions

tel-04877497 , version 1 (09-01-2025)

Identifiants

  • HAL Id : tel-04877497 , version 1

Citer

Paulo Carrillo Rouse. Index theory via deformation groupoids. Mathematics [math]. Université Paul Sabatier (Toulouse 3), 2023. ⟨tel-04877497⟩
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