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$L^2$-cohomology of buildings with fundamental class


Author: Jan Dymara
Journal: Proc. Amer. Math. Soc. 132 (2004), 1839-1843
MSC (2000): Primary 58J22; Secondary 20F55, 20F65
DOI: https://doi.org/10.1090/S0002-9939-03-07234-4
Published electronically: October 15, 2003
MathSciNet review: 2051148
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Abstract: For an infinite building whose Davis chamber is an orientable, gallery connected pseudomanifold (with boundary), we calculate the top- dimensional $L^2$-Betti number. This gives a complete determination of $L^2$-Betti numbers for 2-dimensional, right-angled hyperbolic buildings.


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Additional Information

Jan Dymara
Affiliation: Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wro- cław, Poland
Email: dymara@math.uni.wroc.pl

DOI: https://doi.org/10.1090/S0002-9939-03-07234-4
Received by editor(s): June 12, 2002
Received by editor(s) in revised form: February 10, 2003
Published electronically: October 15, 2003
Additional Notes: This work was partially supported by KBN grant 5 P03A 035 20
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2003 American Mathematical Society

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