We introduce a set of combinatorial techniques for studying the simplicial bounded
cohomology of semi-simplicial sets, simplicial complexes and posets. We apply these …

The study of manifolds and invariants of manifolds was begun more than a century ago. In
this entry we shall discuss the parametrised setting: invariants of families of manifolds …

We compute the abelianisations of the mapping class groups of the manifolds W_g^ 2n= g
(S^ n * S^ n) W g 2 n= g (S n× S n) for n ≥ 3 n≥ 3 and g ≥ 5 g≥ 5. The answer is a direct …

In this work we relate the known results about the homotopy type of classifying spaces for
smooth foliations, with the homology and cohomology of the discrete group of …

We prove that homological stability fails for the moduli space of any simplyconnected closed
smooth 4-manifold in any degree of homology, unlike what happens in all dimensions‰ 4 …

We answer affirmatively a question posed by Morita on homological stability of surface
diffeomorphisms made discrete. In particular, we prove that C∞–diffeomorphisms of …

Morita showed that for each power of the Euler class, there are examples of flat $\mathbb
{S}^ 1$-bundles for which the power of the Euler class does not vanish. Haefliger asked if …

For an oriented manifold $ M $ whose dimension is less than $4 $, we use the contractibility
of certain complexes associated to its submanifolds to cut $ M $ into simpler pieces in order …

Motivated by a question of Ghys, we study obstructions to extending group actions on the
boundary ∂ M∂ M of a 3-manifold to a C^ 0 C 0-action on M. Among other results, we show …

In this paper, we generalize the original idea of Thurston for the so-called Mather-Thurston's
theorem for foliated bundles to prove new variants of this theorem for PL homeomorphisms …