×

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

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

Citations:

Zbl 0566.57020
PDF BibTeX XML Cite
Full Text: DOI EuDML