Geodesic
Boundary values, random walks, and $\ell^p$-cohomology in degree one
Antoine Gournay1
1Université de Neuchâtel, Switzerland
Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1153-1184

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DOI

The vanishing of reduced l2-cohomology for amenable groups can be traced to the work of Cheeger and Gromov in [10]. The subject matter here is reduced lp-cohomology for p∈]1,∞[, particularly its vanishing. Results for the triviality of lpH​1(G) are obtained, for example: when p∈]1,2] and G is amenable; when p∈]1,∞[ and G is Liouville (e.g. of intermediate growth).
DOI : 10.4171/ggd/337
Classification : 20-XX, 05-XX, 31-XX, 60-XX
Mots-clés : Group cohomohology, Lp-cohomology, harmonic functions, Poisson boundary

Antoine Gournay  1

1 Université de Neuchâtel, Switzerland 
Antoine Gournay. Boundary values, random walks, and $\ell^p$-cohomology in degree one. Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1153-1184. doi: 10.4171/ggd/337
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     pages = {1153--1184},
     year = {2015},
     volume = {9},
     number = {4},
     doi = {10.4171/ggd/337},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/337/}
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