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1 vote
1 answer
169 views

Lie group framing and framed bordism

What is the definition of Lie group framing, in simple terms? Is the Lie group framing of spheres a particular type of Lie group framing? (How special is the Lie group framing of spheres differed ...
zeta's user avatar
  • 447
6 votes
1 answer
550 views

Cobordism cohomology of Lie groups

Are there any results about cobordism cohomology of Lie groups?For example, $\mathrm{MU}^*(\mathrm{SU}(n))$.
wushilp's user avatar
  • 61
13 votes
0 answers
317 views

How does quotienting by a finite subgroup act on the framed-cobordism class of a group manifold?

Let $G$ be a connected simple connected compact Lie group, and $\Gamma \subset G$ a finite subgroup. Then (the underlying manifold of) $G$ can be framed by right-invariant vector fields, and this ...
Theo Johnson-Freyd's user avatar
9 votes
0 answers
130 views

Relating bordism groups of $\Omega_{d}^{Spin_c}$ and $\Omega_{d}^{(Spin \times SU(N))/\mathbb{Z}_2}$ to that of $U(N)$

I felt that the earlier question may be too challenging, so let me provide a different angle and more infos to tackle an easier and separate problem. Let us consider a more explicit a short exact ...
wonderich's user avatar
  • 10.4k
6 votes
0 answers
122 views

Bordism groups and a short exact sequence

Let us consider a short exact sequence: $$ 1\to N\to G\to Q \to 1, $$ where $N$, $Q$, and $G$ can be continuous Lie groups in general (or finite groups). Suppose I have the data and the computations ...
wonderich's user avatar
  • 10.4k