Geodesic
Eilenberg swindles and higher large scale homology of products of trees
Francesca Diana1 ; Piotr W. Nowak2 orcid
1Universität Regensburg, Germany
2Polish Academy of Sciences, Warsaw, Poland
Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 371-392

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DOI

We show that uniformly finite homology of products of n trees vanishes in all degrees except degree n, where it is infinite dimensional. Our method is geometric and applies to several large scale homology theories, including almost equivariant homology and controlled coarse homology. As an application we determine group homology with l∞​-coefficients of lattices in products of trees. We also show a characterization of amenability in terms of 1-homology and construct aperiodic tilings using higher homology.
DOI : 10.4171/ggd/400
Classification : 20-XX, 55-XX
Mots-clés : Uniformly finite homology, coarse homology, cohomology of groups, products of trees

Francesca Diana  1   ; Piotr W. Nowak  2

1 Universität Regensburg, Germany
2 Polish Academy of Sciences, Warsaw, Poland 
Francesca Diana; Piotr W. Nowak. Eilenberg swindles and higher large scale homology of products of trees. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 371-392. doi: 10.4171/ggd/400
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     title = {Eilenberg swindles and higher large scale homology of products of trees},
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     year = {2017},
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     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/400/}
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