What type of study is this?

This is a Literature Review study.

August 17, 2025

On 𝐻* (𝐵𝑃𝑈👺;ℤ) and Weyl group invariants

Key Points

The integral restriction homomorphism is onto for projective unitary groups, linking distinct invariants.
Key evidence includes the successful demonstration of invariants in several naturally isomorphic rings.
Assessment uses homomorphisms relating to the structure of connected compact Lie groups.
Findings may enhance understanding of group actions and integral invariants, suggesting broader implications in topology.

Abstract

For the projective unitary group P U n PUₙ with a maximal torus T P U n T₏ₔ䂸 and Weyl group W W, we show that the integral restriction homomorphism \ ρ P U n: H ∗ (B P U n ; Z) → H ∗ (B T P U n ; Z) W ₏ₔ䂸 H^* (BPUₙ; Z) H^* (BT₏ₔ䂸; Z) W \ to the integral invariants of the Weyl group action is onto. We also present several rings naturally isomorphic to H ∗ (B T P U n ; Z) W H^* (BT₏ₔ䂸; Z) W. In addition we give general sufficient conditions for the restriction homomorphism ρ G G to be onto for a connected compact Lie group G G.

Mark Helpful

Bookmark

Relay