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Bounded cohomology of lattices in higher rank Lie groups

Marc Burger, Nicolas Monod (1999)

Journal of the European Mathematical Society

We prove that the natural map H b 2 ( Γ ) H 2 ( Γ ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ : the stable commutator length vanishes and any C 1 –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating H * b ( Γ ) to the continuous bounded cohomology of the ambient group...

Brown–Peterson cohomology and Morava K-theory of DI(4) and its classifying space

Marta Santos (1999)

Fundamenta Mathematicae

DI(4) is the only known example of an exotic 2-compact group, and is conjectured to be the only one. In this work, we study generalized cohomology theories for DI(4) and its classifying space. Specifically, we compute the Morava K-theories, and the P(n)-cohomology of DI(4). We use the non-commutativity of the spectrum P(n) at p=2 to prove the non-homotopy nilpotency of DI(4). Concerning the classifying space, we prove that the BP-cohomology and the Morava K-theories of BDI(4) are all concentrated...

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