Speaker: Dr. Sushil Bhunia

Title of the Talk: Twisted Conjugacy Classes in Groups

Date, Time and Venue: 19th March 2025, 12:00 PM, at LHC II - room no. 101

Abstract: Abstract: Let G be a group and Aut(G) denote the group of automorphisms of G. Let φ ∈ Aut(G). Two elements x and y of G are said to be φ-twisted conjugate if y = gxφ(g)−1 for some g in G. This is an equivalence relation on G, and the equivalence classes are called φ-twisted conjugacy classes or Reidemeister classes of φ. If φ = Id, then the φ-twisted conjugacy classes are the usual conjugacy classes. A group G is said to have the R∞-property if the number of its φ-twisted conjugacy classes is infinite for all φ ∈ Aut(G). In this talk, we will discuss the following: (1) a connected linear algebraic group G has the (algebraic) R∞-property if and only if the fixed point subgroup Gφ is infinite for all (algebraic) group automorphism φ of G. If time permits, we shall discuss the following theorem. (2) We prove that the big mapping class group has the R∞-property under some suitable conditions on the infinite-type surface.