# Tagged Questions

**3**

votes

**0**answers

109 views

### spectral sequence differential for cobordism

From page 6 of these solutions:
the differential\begin{equation}d_2: H_p(X,\Omega_1^{Spin})\rightarrow H_{p-2}(X,\Omega_2^{Spin})\end{equation}connecting the 1-st and the 2-nd row is the ...

**7**

votes

**1**answer

275 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

**2**answers

167 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

**1**answer

469 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

**1**answer

391 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

**2**answers

558 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 ...