Construction of spaces for which every homeomorphism can be deformed toa fixed point free map | BIMSA Topology Seminar

Abstract

(this is joint work with Peter Wong, Bates College-USA). Few years ago it was discovered afamily of Nilmanifolds with the property that every homeomorphism of a manifold of the family canbe deformed to a homeomorphism which is fixed point free. These spaces satisfy a property whichcan be regarded the opposity of the fixed point property. The examples above are K(m, 1). We willshow new examples of spaces which satisfies the property above which manifolds and they are noiK(n, 1). The spaces constructed are mapping torus of certain lens space. The description of themethod open the possibility of further examples. We describe in more properties and calculation oithe Reidemeister classes, which play an important role in the solution of the problem. Follows a fewrelevant references.

I1] Gonccalves, Daciberg; Wong, Peter: Twisted conjugacy classes in nilpotent groups. J. ReineAngew. Math.633 (2009),1127.

[2] Gonic calves, Daciberg; Wong, Peter: Twisted conjugacy for virtually cyclic groups andcrystallographic groups. Combinatorial and geometric group theory, 119147, Trends Math.Birkhuser/Springer Basel AG, Basel, 2010.

[3] Sun, Hongbin: Degree`1 self-maps and self-homeomorphisms on prime 3manifolds. Algebraicand Geometric Topology 10 (2010) 867890.[4] Pan, Xiaotian; Hou, Bingzhe; Zhang, Zhongyang: Self-homeomorphisms and degree ±l selfmaps on lens spaces. Bull. lranian Math.Soc. 45(2019), no.6,18551869.