nLab Spin geometry


This page collects links related to the book

on spin geometry.


Chapter I Clifford algebras, Spin groups and Their Representations

1 Clifford algebras

2 The group PinPin and SpinSpin

3 The algebras CL nCL_n and Cl r,sCl_{r,s}

4 Classification

5 Representations

6 Lie algebra structures

7 Some direct applications to geometry

8 Some further applications to the theory of Lie groups

9 K-Theory and the Atiyah-Bott-Shapiro construction

10 KR-theory and the (1,1)(1,1)-Periodicity theorem

Chapter II Spin Geometry and the Dirac Operator

1 Spin structures on vector bundles

2 Spin manifolds and Spin cobordism

  • spin cobordism?

3 Clifford and spinor bundle

4 Connection on spinor bundle

5 The Dirac operators

6 The fundamental elliptic operators

7 Cl kCl_k-linear Dirac operators

8 Vanishing theorems and some applications

Chapter III Index Theorems

Chapter IV Applications in Geometry and Topology

category: reference

Last revised on April 26, 2020 at 10:34:44. See the history of this page for a list of all contributions to it.