Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck - Couverture souple

Bismut, Jean-Michel; Shen, Shu; Wei, Zhaoting

Couverture souple

ISBN 10 : 3031272366 ISBN 13 : 9783031272363

Editeur : Birkhäuser, 2024

Synopsis

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian.
Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource formany researchers in geometry, analysis, and mathematical physics.

A propos du livre

À propos de l'auteur

​Jean-Michel Bismut is a French mathematician who is a professor in the Mathematics Department in Orsay. He is known for his contributions to index theory, geometric analysis and probability theory. Together with Gilles Lebeau, he has developed the theory of the hypoelliptic Laplacian, to which he found applications in various fields of mathematics. He shared the Shaw Prize in Mathematical Sciences 2021 with Jeff Cheeger.
Shu Shen is a maître de conférences at Sorbonne University in Paris. His research focuses on the fields of analysis, geometry, and representation theory.
Zhaoting Wei is an assistant professor in mathematics at Texas A&M University-Commerce, USA. His research interests include noncommutative geometry and higher category theory.

Détails de l'édition

• Éditeur: Birkhäuser
• Date d'édition: 2024
• Langue: anglais
• ISBN 10: 3031272366
• ISBN 13: 9783031272363
• Reliure: Broché
• Nombre de pages: 196
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne