5
votes
2answers
489 views

index of a family of Dirac operators in $K^1$

Suppose I have a family of Dirac operators over a compact base space B. From the paper of Atiyah and Singer about skew adjoint Fredholm operators we know that it has an index in $K^1(B)$. Suppose ...
3
votes
1answer
198 views

The space of spectral sections and connections to K-theory

We look at a familiy $D_\alpha$ of Dirac operators over a (compact) base space B. The projection $\Pi^+_\alpha$ onto the positive eigenspaces of $D_\alpha$ is usually not continuous in α. ...