Atiyah’s L2-index theorem, Kan-Thurston construction, and weak Bass conjecture

We conjecture that for a group G of type FP , the L 2 -Euler characteristic of a group G is the same as the ordinary Euler characteristic of G , and show that this conjecture is closely related with the weak Bass conjecture. We also present a class of groups satisfying this conjecture. Ourmethod com...

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Bibliographic Details
Published in:Boletim da Sociedade Brasileira de Matemática 2014, Vol.45 (2), p.355-369
Main Author: Jo, Jang Hyun
Format: Article
Language:English
Subjects:
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We conjecture that for a group G of type FP , the L 2 -Euler characteristic of a group G is the same as the ordinary Euler characteristic of G , and show that this conjecture is closely related with the weak Bass conjecture. We also present a class of groups satisfying this conjecture. Ourmethod combines the Kan-Thurston construction, Atiyah’s L 2 -index theorem, and a result of Berrick, Chatterji, and Mislin.
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-014-0053-y