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Coherent Sheaves Superconnections and Riemann Roch Grothendieck 2023rd Edition by Jean Michel Bismut, Shu Shen, Zhaoting Wei 9783031272332 3031272331

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Coherent Sheaves Superconnections and Riemann Roch Grothendieck 2023rd Edition Jean-Michel Bismut Digital Instant Download

Author(s): Jean-Michel Bismut, Shu Shen, Zhaoting Wei
ISBN(s): 9783031272332, 3031272331
Edition: 2023
File Details: PDF, 2.32 MB
Year: 2023
Language: english
SKU: EB-57783794 Category: Tags: , ,

Coherent Sheaves Superconnections and Riemann Roch Grothendieck 2023rd Edition by Jean Michel Bismut, Shu Shen, Zhaoting Wei – Ebook PDF Instant Download/Delivery: 9783031272332, 3031272331

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Product details:

ISBN 10: 3031272331

ISBN 13: 9783031272332

Author: Jean-Michel Bismut, Shu Shen, Zhaoting Wei

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.

Table of contents:

Chapter 1: Introduction

Chapter 2: Bott-Chern Cohomology and Characteristic Classes

Chapter 3: The Derived Category

Chapter 4: Preliminaries on Linear Algebra and Differential Geometry

Chapter 5: The Antiholomorphic Superconnections of Block

Chapter 6: An Equivalence of Categories

Chapter 7: Antiholomorphic Superconnections and Generalized Metrics

Chapter 8: Generalized Metrics and Chern Character Forms

Chapter 9: The Case of Embeddings

Chapter 10: Submersions and Elliptic Superconnections

Chapter 11: Elliptic Superconnection Forms and Direct Images

Chapter 12: A Proof of Theorem 10-1 when

Chapter 13: The Hypoelliptic Superconnections

Chapter 14: The Hypoelliptic Superconnection Forms

Chapter 15: The Hypoelliptic Superconnection Forms when

Chapter 16: Exotic Superconnections and Riemann-Roch-Grothendieck

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Tags: Jean Michel Bismut, Shu Shen, Zhaoting Wei, Grothendieck