7
votes
1answer
253 views

Reference request: Spin structures on surfaces and the spin mapping class group

I am looking for references on the following: Spin structures on surfaces, and particularly the spin mapping class group. What is known about generating the spin mapping class group? Has anybody ...
7
votes
2answers
159 views

is there an anyon structure analogous to spin structure for rank 2 bundle?

A spin structure on a Riemannian bundle of rank >2 is the lift of the structure group from $\text{SO}(n)$ to its universal cover $\text{Spin}(n).$ It may also be defined in the case $n=2$ as the lift ...
5
votes
1answer
427 views

Atiyah-Bott-Shapiro Orientation

Dear community, there are so-called orientation maps $a:MSpin\to ko$ and $b:MSpin^c \to k$, "defined" in ABS's paper "Clifford modules". Unfortunately I am not familiar with representation theory. ...
4
votes
1answer
385 views

Spin structures and quadratic forms on surfaces

In his paper "Spin structures and quadratic forms on surfaces", Johnson constructs a bijection between the set of spin strucutres on a smooth closed orientable surface $S$ and the set of quadratic ...
13
votes
2answers
548 views

Spin structures on 7-dimensional spherical space forms

Background Let $M$ be a spin manifold and let $\Gamma$ be a finite group acting freely and isometrically on $M$ in such a way that $M/\Gamma$ is a smooth riemannian manifold. The quotient will be ...