##### Department of Mathematics,

University of California San Diego

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### Group Actions Seminar

## Octave Lacourte - Graduate student

#### Claude Bernard Lyon 1 University

## A signature for some subgroups of the permutation group of [0,1[

##### Abstract:

For every infinite set X we define S(X) as the group of all permutations of X. On its subgroup consisting of all finitely supported permutations there exists a natural group homomorphism signature. However, thanks to an observation of Vitali in 1915, we know that this group homomorphism does not extend to S(X). In the talk we extend the signature on the subgroup of S(X) consisting of all piecewise isometric elements (strongly related to the Interval Exchange Transformation group). This allows us to list all of its normal subgroups and gives also informations about an element of the second cohomology group of some groups.

Host: Brandon Seward

### November 10, 2020

### 9:00 AM

### Zoom ID 967 4109 3409 (email Nattalie Tamam or Brandon Seward for the password)

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