Fixed point theory for homogeneous spaces, II

• Autorzy: Peter Wong
• Języki publikacji: EN

Abstrakty

EN

Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously known under the hypothesis that p⁎: Hₙ(G) → Hₙ(M) is nontrivial where n = dim M. A simple formula using equivariant degree is given for the Reidemeister trace of a selfmap f: M → M.

Kategorie tematyczne

• 55M20: Fixed points and coincidences
• 57S99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2005
• Tom: 186
• Numer: 2
• Strony: 161-175

Daty

wydano

2005

Twórcy

autor

Peter Wong

• Department of Mathematics Bates College, Lewiston, ME 04240, U.S.A.

Identyfikatory

DOI

10.4064/fm186-2-4