Pure Maths Colloquium - Fixed points, Twisted Conjugacy and Lie Algebras - Prof Karel Dekimpe (Leuven) Seminar
- Time:
- 15:00 - 16:00
- Date:
- 16 March 2018
- Venue:
- Lecture Theatre 20C, Room 10031, Building 54, Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ
For more information regarding this seminar, please email Dr Jan Spakula at J.Spakula@southampton.ac.uk .
Event details
Abstract: Let G be a group and p:G -> G be a morphism. We will say that two elements x and y are twisted conjugate if x = z y p(z)^(-1)$ for some z in G. Note that when p is the identity on G, the notion of twisted conjugacy reduces to that of ordinary conjugacy. The number of twisted conjugacy classes is called the Reidemeister number of p and is denoted by R(p). Now, let f:X -> X be a self map of a closed manifold X. In this talk I will explain how the number of fixed points of f is related to the number of twisted conjugacy classes R(f_*). Here f_* is the endomorphism of the fundamental group of X induced by f. Finally, I will show how Lie algebra techniques can be used to easily compute those Reidemeister numbers.
Speaker information
Professor Karel Dekimpe , KU Leuven. Topics: Almost-crystallographic groups and infra-nilmanifolds: Expanding maps, Anosov diffeomorphisms, Nielsen fixed point theory, Automorphisms of virtually nilpotent groups and more general groups, Twisted conjugacy, The R infinity property, Nilpotent and solvable Lie groups and Lie algebras Involved in the Methusalem Project in Pure Mathematics of the KU Leuven (with yearly calls for PhD students and postdoctoral researchers.)