On $H^*(BPU_n; \mathbb{Z})$ and Weyl group invariants
Abstract
For the projective unitary group $PU_n$ with a maximal torus $T_{PU_n}$ and Weyl group $W$, we show that the integral restriction homomorphism \[\rho_{PU_n} \colon H^*(BPU_n;\mathbb{Z})\rightarrow H^*(BT_{PU_n};\mathbb{Z})^W\] to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to $H^*(BT_{PU_n};\mathbb{Z})^W$. In addition we give general sufficient conditions for the restriction homomorphism $\rho_G$ to be onto for a connected compact Lie group $G$.
 Publication:

arXiv eprints
 Pub Date:
 March 2021
 DOI:
 10.48550/arXiv.2103.03523
 arXiv:
 arXiv:2103.03523
 Bibcode:
 2021arXiv210303523C
 Keywords:

 Mathematics  Algebraic Topology;
 55R35;
 55R40;
 55T10
 EPrint:
 18 pages. Minor corrections