Geodesic
On a family of unitary representations of mapping class groups
Biao Ma1
1Université Côte d’Azur, Nice, France
Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1399-1420

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DOI

For a compact surface S=Sg,n​ with 3g+n≥4, we introduce a family of unitary representations of the mapping class group Mod(S) based on the space of measured foliations. or this family of representations, we show that none of them has almost invariant vectors. As one application, we obtain an inequality concerning the action of Mod(S) on the Teichmüller space of S. Moreover, using the same method plus recent results about weak equivalence, we also give a classification, up to weak equivalence, for the unitary quasi-representations with respect to geometrical subgroups.
DOI : 10.4171/ggd/634
Classification : 20-XX, 22-XX
Mots-clés : Mapping class groups, measured foliations, unitary representations, almost invariant vectors, almost properly discontinuous, weak containment

Biao Ma  1

1 Université Côte d’Azur, Nice, France 
Biao Ma. On a family of unitary representations of mapping class groups. Groups, geometry, and dynamics, Tome 15 (2021) no. 4, pp. 1399-1420. doi: 10.4171/ggd/634
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     title = {On a family of unitary representations of mapping class groups},
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     pages = {1399--1420},
     year = {2021},
     volume = {15},
     number = {4},
     doi = {10.4171/ggd/634},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/634/}
}
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