The spectrum of Laplace operators and finite approximations of infinite groups

• Applicant: Professor Dr. Roman Sauer
• Subject Area: Mathematics
• Term: from 2011 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 207558863

The zero-in-the-spectrum conjecture by Gromov, which is implied by the Novikov conjecture, says that the (non-reduced) l2-homology of closed aspherical manifolds vanishes. For quite a while it remained open whether this conjecture is true under much more general assumptions. One may consider two directions of generalization: a) one drops the condition of being aspherical or b) one replaces closed aspherical manifolds by classifying spaces of groups that satisfy certain finiteness conditions. The generalization a) was falsified by a counterexample of Farber and Weinberger. In this project we shall study a certain class of operad groups whose l2-homology vanishes. In particular, they provide counterexamples to b). Further, we shall study finiteness results for operad groups which unify and generalize numerous results in the literature.

• DFG Programme: Research Grants