Notes on the group of \(S^ 1\) equivariant homeomorphisms (Q1918533)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Notes on the group of \(S^ 1\) equivariant homeomorphisms |
scientific article; zbMATH DE number 906885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Notes on the group of \(S^ 1\) equivariant homeomorphisms |
scientific article; zbMATH DE number 906885 |
Statements
Notes on the group of \(S^ 1\) equivariant homeomorphisms (English)
0 references
18 July 1996
0 references
Let \(P\) be a principal \(S^1\)-bundle over a compact manifold \(X\) with first Betti number \(b_1(X)=0\). The author studies the group \(\text{Homeo}_{S^1}(P)\) of \(S^1\) equivariant homeomorphisms of \(P\). In particular, let \(P_k\) be the principal \(S^1\)-bundle over \(\mathbb{C} P^n\) with \(c_1(P_k)=k\). Then Theorem. \(\pi_{2i+1}(\text{Homeo}_{S^1}(P_k))\) has a free part for \(i=0,1,\dots,n\). A similar result holds for \(S^3\)-bundles over \(\mathbb{H} P^n\).
0 references
principal bundle
0 references
compact manifold
0 references
equivariant homeomorphisms
0 references
0 references
0.8236923217773438
0 references
0.8202543258666992
0 references
0.7277005910873413
0 references
