nLab Spin geometry

This page collects links related to the book

• H. Blaine Lawson, Marie-Louise Michelsohn

  Spin geometry

  Princeton University Press (1989)

  ISBN 9780691085425

on spin geometry.

Chapter I Clifford algebras, Spin groups and Their Representations

1 Clifford algebras

• Clifford algebra

2 The group $Pin$ and $Spin$

• spin group

3 The algebras $CL_n$ and $Cl_{r,s}$

4 Classification

5 Representations

• spin representation

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

• K-theory

• Atiyah-Bott-Shapiro isomorphism

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

• KR-theory

Chapter II Spin Geometry and the Dirac Operator

1 Spin structures on vector bundles

• spin structure

2 Spin manifolds and Spin cobordism

• spin cobordism?

3 Clifford and spinor bundle

• Clifford bundle

• spinor bundle

4 Connection on spinor bundle

• connection on a bundle

• spin connection

5 The Dirac operators

• Dirac operator

6 The fundamental elliptic operators

• elliptic operator

7 $Cl_k$-linear Dirac operators

• fiber integration in K-theory

• index

8 Vanishing theorems and some applications

Chapter III Index Theorems

• index theory

• index of a Dirac operator

Chapter IV Applications in Geometry and Topology

• spin geometry

category: reference