## 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

### Keywords:

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

Zbl 0566.57020
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