Fixed point theory for homogeneous spaces, II

Peter Wong. "Fixed point theory for homogeneous spaces, II." Fundamenta Mathematicae 186.2 (2005): 161-175. <http://eudml.org/doc/283237>.

@article{PeterWong2005,
abstract = {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.},
author = {Peter Wong},
journal = {Fundamenta Mathematicae},
keywords = {Lefschetz number; Nielsen number; Reidemeister trace; root theory; homogeneous space},
language = {eng},
number = {2},
pages = {161-175},
title = {Fixed point theory for homogeneous spaces, II},
url = {http://eudml.org/doc/283237},
volume = {186},
year = {2005},
}

TY - JOUR
AU - Peter Wong
TI - Fixed point theory for homogeneous spaces, II
JO - Fundamenta Mathematicae
PY - 2005
VL - 186
IS - 2
SP - 161
EP - 175
AB - 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.
LA - eng
KW - Lefschetz number; Nielsen number; Reidemeister trace; root theory; homogeneous space
UR - http://eudml.org/doc/283237
ER -