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 …

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 …

Motivated by the operad built from moduli spaces of Riemann surfaces, we consider a
general class of operads in the category of spaces that satisfy certain homological stability …

We prove a general representation stability result for polynomial coefficient systems which
lets us prove representation stability and secondary homological stability for many families …

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 …

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 …

We prove that the group homology of the diffeomorphism group of# g S n× S n\int (D 2 n) as
a discrete group is independent of g in a range, provided that n> 2. This answers the high …

We establish a form of the h–principle for the existence of foliations of codimension at least 2
which are quasicomplementary to a given one. Roughly,“quasicomplementary” means that …

PL homeomorphisms of surfaces and codimension 2 PL foliations Page 1 PL homeomorphisms
of surfaces and codimension 2 PL foliations Sam Nariman Compositio Math. 160 (2024) …

We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold
bundles. In this context, Haefliger-Thurston's conjecture predicts that every $ M $-bundle …