Close PL involutions of 3-manifolds have close fixed point sets: 1- dimensional components. (English) Zbl 0566.57021

Jakobsche, W.

Fundam. Math. 116, 83-91 (1983).

Let M be a closed PL 3-manifold and \(\rho\) be a metric on the space M. The main theorem of this paper is: Let f be a PL involution on M. Then for every \(\epsilon >0\) there exists an \(\eta >0\) such that for every PL involution g on M satisfying \(\sup_{x\in M}(\rho (f(x),g(x)))<\eta\) there exists a homeomorphism h: Fix\({}^ 1(f)\to Fix^ 1(g)\) such that \(\sup_{x\in Fix^ 1(f)}(\rho (x,h(x)))<\epsilon\). \(Fix^ 1(f)\) denotes the union of all 1-dimensional components of the fixed-point set of f.

Reviewer: P.Kim

MSC:

57S17	Finite transformation groups
57N10	Topology of general \(3\)-manifolds (MSC2010)
57S25	Groups acting on specific manifolds
57Q37	Isotopy in PL-topology

Keywords:

closed PL 3-manifold; PL involution; fixed-point set

Citations:

Zbl 0566.57020