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BIMSA Topology Seminar
Construction of spaces for which every homeomorphism can be deformed to a fixed point free map
Construction of spaces for which every homeomorphism can be deformed to a fixed point free map
Organizers
Speaker
Daciberg Goncalves
Time
Wednesday, March 27, 2024 1:00 PM - 2:00 PM
Venue
A3-4-101
Online
Zoom 559 700 6085
(BIMSA)
Abstract
(this is joint work with Peter Wong, Bates College-USA). Few years ago it was discovered a family of Nilmanifolds with the property that every homeomorphism of a manifold of the family can be deformed to a homeomorphism which is fixed point free. These spaces satisfy a property which can be regarded the opposity of the fixed point property. The examples above are $K(\pi,1)$. We will show new examples of spaces which satisfies the property above which manifolds and they are not $K(\pi,1)$. The spaces constructed are mapping torus of certain lens space. The description of the method open the possibility of further examples. We describe in more properties and calculation of the Reidemeister classes, which play an important role in the solution of the problem. Follows a few relevant references.
[1] Gonccalves, Daciberg; Wong, Peter: Twisted conjugacy classes in nilpotent groups. J. Reine Angew. Math. 633 (2009), 11–27.
[2] Gon\c calves, Daciberg; Wong, Peter: Twisted conjugacy for virtually cyclic groups and crystallographic groups. Combinatorial and geometric group theory, 119–147, Trends Math., Birkhäuser/Springer Basel AG, Basel, 2010.
[3] Sun, Hongbin: Degree ̇1 self-maps and self-homeomorphisms on prime 3–manifolds. Algebraic and Geometric Topology 10 (2010) 867–890.
[4] Pan, Xiaotian; Hou, Bingzhe; Zhang, Zhongyang: Self-homeomorphisms and degree $\pm1$ self-maps on lens spaces. Bull. Iranian Math. Soc. 45 (2019), no. 6, 1855–1869.
[1] Gonccalves, Daciberg; Wong, Peter: Twisted conjugacy classes in nilpotent groups. J. Reine Angew. Math. 633 (2009), 11–27.
[2] Gon\c calves, Daciberg; Wong, Peter: Twisted conjugacy for virtually cyclic groups and crystallographic groups. Combinatorial and geometric group theory, 119–147, Trends Math., Birkhäuser/Springer Basel AG, Basel, 2010.
[3] Sun, Hongbin: Degree ̇1 self-maps and self-homeomorphisms on prime 3–manifolds. Algebraic and Geometric Topology 10 (2010) 867–890.
[4] Pan, Xiaotian; Hou, Bingzhe; Zhang, Zhongyang: Self-homeomorphisms and degree $\pm1$ self-maps on lens spaces. Bull. Iranian Math. Soc. 45 (2019), no. 6, 1855–1869.