95 citations · 393 across the 27 of their papers we have counts for
22 papers · 1 filter
Algebraic independence of topological Pontryagin classes
Soren Galatius, Oscar Randal-Williams
We show that the topological Pontryagin classes are algebraically independent in the rationalised cohomology of BTop(d) for all .
-cells and general linear groups of infinite fields
Soren Galatius, Alexander Kupers, Oscar Randal-Williams
We study the general linear groups of infinite fields (or more generally connected semi-local rings with infinite residue fields) from the perspective of -algebras. We pr…
Operations on stable moduli spaces
Soren Galatius, Oscar Randal-Williams
We construct certain operations on stable moduli spaces and use them to compare cohomology of moduli spaces of closed manifolds with tangential structure. We obtain isomorphisms in…
Moduli spaces of manifolds: a user's guide
Soren Galatius, Oscar Randal-Williams
We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked exam…
-cells and general linear groups of finite fields
Soren Galatius, Alexander Kupers, Oscar Randal-Williams
We prove new homological stability results for general linear groups over finite fields. These results are obtained by constructing CW approximations to the classifying spaces of t…
The Equivariant Cobordism Category
Gergely Szűcs, Søren Galatius
For a finite group , we define an equivariant cobordism category . Objects of the category are -dimensional closed smooth -manifolds and morphisms are…
-cells and mapping class groups
Soren Galatius, Alexander Kupers, Oscar Randal-Williams
We prove a new kind of stabilisation result, "secondary homological stability", for the homology of mapping class groups of orientable surfaces with one boundary component. These r…
Homological stability for moduli spaces of high dimensional manifolds. II
Soren Galatius, Oscar Randal-Williams
We prove a homological stability theorem for moduli spaces of manifolds of dimension , for attaching handles of index at least , after these manifolds have been stabilised b…
Tautological rings for high dimensional manifolds
Soren Galatius, Ilya Grigoriev, Oscar Randal-Williams
We study tautological rings for high dimensional manifolds, that is, for each smooth manifold the ring of those of characteristic classes of smooth fibre bundles with…
Abelian quotients of mapping class groups of highly connected manifolds
Soren Galatius, Oscar Randal-Williams
We compute the abelianisations of the mapping class groups of the manifolds for and . The answer is a direct sum of two parts. T…
Homological stability for moduli spaces of high dimensional manifolds. I
Soren Galatius, Oscar Randal-Williams
We prove a homological stability theorem for moduli spaces of simply-connected manifolds of dimension , with respect to forming connected sum with . This is…
Detecting and realising characteristic classes of manifold bundles
Soren Galatius, Oscar Randal-Williams
We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic…
Homological stability for moduli spaces of high dimensional manifolds
Soren Galatius, Oscar Randal-Williams
We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homolo…
Stable moduli spaces of high dimensional manifolds
Soren Galatius, Oscar Randal-Williams
We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whos…
Monoids of moduli spaces of manifolds
Soren Galatius, Oscar Randal-Williams
We study categories of d-dimensional cobordisms from the perspective of Tillmann and Galatius-Madsen-Tillmann-Weiss. There is a category of closed smooth (d-1)-manifolds and…
Universal moduli spaces of surfaces with flat connections and cobordism theory
Ralph L. Cohen, Soren Galatius, Nitu Kitchloo
Given a semisimple, compact, connected Lie group G with complexification G^c, we show there is a stable range in the homotopy type of the universal moduli space of flat connections…
Divisibility of the stable Miller-Morita-Mumford classes
Soren Galatius, Ib Madsen, Ulrike Tillmann
We determine the sublattice generated by the Miller-Morita-Mumford classes in the torsion free quotient of the integral cohomology ring of the stable mapping class group. We…
Stable homology of automorphism groups of free groups
Soren Galatius
Homology of the group Aut(F_n) of automorphisms of a free group on n generators is known to be independent of n in a certain stable range. Using tools from homotopy theory, we prov…
The homotopy type of the cobordism category
Soren Galatius, Ib Madsen, Ulrike Tillmann +1
The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in order to formalize the concept of field theories…
Mod 2 homology of the stable spin mapping class group
Soren Galatius
We compute the mod 2 homology of spin mapping class groups in the stable range. In earlier work we computed the stable mod p homology of the oriented mapping class group, and the m…
Secondary Characteristic Classes of Surface Bundles
Soren Galatius
The Miller-Morita-Mumford classes associate to an oriented surface bundle a class . In this note we define for each prime and each integer $i\…
Mod p homology of the stable mapping class group
Soren Galatius
We calculate the homology of the mapping class group in the stable range. The calculation is based on Madsen and Weiss' proof of the "Generalised Mumford Conjecture".