El proper dimecres, 6 dabril, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).
Speaker: Jordi Daura Serrano
Universitat: Universitat de Barcelona
Data: Wednesday, April 6th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: UB (FMI, aula B1) and Zoom
Títol: Degree of symmetry of manifolds and the toral rank conjecture
Resum: The aim of the theory of transformation groups is to study the symmetry of spaces like manifolds, by studying group actions on them. One of the fundamental questions is the following: given a manifold M, how “big” a compact Lie group acting effectively on M can be? Although the most well-known manifolds are highly symmetric, like spheres and tori, it is conjectured that most manifolds admit few or no compact group actions. In order to make this question more precise,
it is possible to associate to a manifold its degree of symmetry, a value which tells us how symmetric this manifold is. Moreover, we may try to compute it by using topological and geometric information of the manifold. These type of computations are really hard and they lead to interesting questions, like the toral rank conjecture, formulated by S.Halperin in 1985. In the first part of the talk will be a brief introduction to the theory of compact transformation groups and the
various definitions of degree of symmetry, while in the second part I will explain the statement of the toral rank conjecture.
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