Preprints

A vanishing theorem for tautological classes of aspherical manifolds ( ArXiV), with Fabian Hebestreit, Markus Land, and Wolfgang Lück.

Semi-simplicial spaces ( ArXiV), with Johannes Ebert.

Some phenomena in tautological rings of manifolds ( ArXiV).

Topology of the Electroweak Vacua ( ArXiV), with Ben Gripaios.


Publications

Homological stability for automorphism groups ( ArXiV), with Nathalie Wahl.
Advances in Mathematics, to appear.

Homological stability for moduli spaces of high dimensional manifolds. I ( ArXiV), with Søren Galatius.
Journal of the American Mathematical Society, to appear. (This supersedes our earlier preprint arXiv:1203.6830.)

Cohomology of automorphism groups of free groups with twisted coefficients ( ArXiV).
Selecta Mathematica, to appear. (This supersedes the earlier preprint arXiv:1012.1433.)

Homological stability for moduli spaces of high dimensional manifolds. II ( ArXiV), with Søren Galatius.
Annals of Mathematics 186 (1) (2017) 127-204.

Infinite loop spaces and positive scalar curvature ( ArXiV), with Boris Botvinnik and Johannes Ebert.
Inventiones mathematicae, to appear.

An upper bound for the pseudoisotopy stable range ( ArXiV).
Mathematische Annalen, 368 (3) (2017), 1081-1094.

Tautological rings for high dimensional manifolds ( ArXiV), with Søren Galatius and Ilya Grigoriev.
Compositio Mathematica 153 (4) (2017) 851-866.

Homological stability for spaces of embedded surfaces ( ArXiV), with Federico Cantero.
Geometry & Topology 21 (2017) 1387-1467.

Abelian quotients of mapping class groups of highly connected manifolds ( ArXiV), with Søren Galatius.
Mathematische Annalen 365 (1) (2016) 857-879.

Resolutions of moduli spaces and homological stability ( ArXiV).
Journal of the European Mathematical Society 18 (2016) 1-81.

Torelli spaces of high-dimensional manifolds ( ArXiV), with Johannes Ebert.
Journal of Topology 8 (1) (2015) 38-64.

Stable moduli spaces of high-dimensional manifolds ( ArXiV), with Søren Galatius.
Acta Mathematica 212 (2014), no. 2, 257-377.
Erratum

Detecting and realising characteristic classes of manifold bundles ( ArXiV), with Søren Galatius.
Algebraic Topology: Applications and New Directions (Stanford, CA, 2012), Contemp. Math.

Generalised Miller-Morita-Mumford classes for block bundles and topological bundles ( ArXiV), with Johannes Ebert.
Algebraic & Geometric Topology 14 (2014) 1181-1204.

"Topological chiral homology" and configuration spaces of spheres.
Morfismos, (MIMS proceedings issue), Vol. 17 No 2 (2013) 57-70.

Homology of the moduli spaces and mapping class groups of framed, r-Spin and Pin surfaces ( ArXiV).
Journal of Topology 7 (1) (2014) 155-186.
Erratum

"Group-Completion", local coefficient systems, and perfection ( Preprint).
Quarterly Journal of Mathematics 64 (3) (2013) 795-803.

The space of immersed surfaces in a manifold ( ArXiV).
Mathematical Proceedings of the Cambridge Philosophical Society 154 (3) (2013) 419-438.

Relations among tautological classes revisited ( ArXiV).
Advances in Mathematics 231 (3-4) (2012) 1773-1785.

The Picard group of the moduli space of r-Spin Riemann surfaces ( ArXiV).
Advances in Mathematics 231 (1) (2012) 482-515.

Stable cohomology of the universal Picard varieties and the extended mapping class group ( ArXiV), with Johannes Ebert.
Documenta Mathematica 17 (2012) 417-450.

Homological stability for unordered configuration spaces ( ArXiV).
Quarterly Journal of Mathematics 64 (1) (2013) 303-326.

Embedded cobordism categories and spaces of submanifolds ( ArXiV).
International Mathematics Research Notices 3 (2011) 572-608.

Monoids of moduli spaces of manifolds ( ArXiV), with Søren Galatius.
Geometry & Topology 14 (2010) 1243-1302.
Erratum

The homology of the stable non-orientable mapping class group ( ArXiV).
Algebraic & Geometric Topology 8 (2008) 1811-1832.
Erratum

On the divisibility of characteristic classes of non-orientable surface bundles ( ArXiV), with Johannes Ebert.
Topology and its Applications 156 (2008) 246-250.


Other documents

On diffeomorphisms acting on almost complex structures, 2015.

The complex of injective words is highly connected, 2015.

A combinatorial identity, 2012.

Cohomology of Aut(F_n) with twisted coefficients, for the "Topologie" Oberwolfach report, 2016.

Stable moduli spaces of high dimensional manifolds, for the "Topologie" Oberwolfach report, 2014.

Homological stability for moduli spaces of manifolds, for the "Topologie" Oberwolfach report, 2012.

Monoids of moduli spaces of manifolds, II, for the "Topologie" Oberwolfach report, 2010.

Monoids of moduli spaces of manifolds, for the "Manifold Perspectives" Oberwolfach report, 2009.

Homological stability for moduli spaces of high dimensional manifolds ( ArXiV), with Søren Galatius .

The stable cohomology of automorphisms of free groups with coefficients in the homology representation ( ArXiV).

Non-triviality of torsion universal characteristic classes of 3-manifold bundles.


Adams E2 pages of Madsen-Tillmann spectra

SpectrumE2 pageModule definition
$\mathbf{MTO}(1)$HereHere
$\mathbf{MTO}(2)$HereHere
$\mathbf{MTSO}(2)$HereHere
$\mathbf{MTSpin}(4)$HereHere
I have computed the (mod 2) Adams E2 terms for the stable homotopy groups of some Madsen-Tillmann spectra. Recall that $\mathbf{MTO}(2)$ and $\mathbf{MTSO}(2)$ are respectively the homotopy-types of the non-orientable and oriented stable mapping class groups, after plus-construction. This uses Robert Bruner's program for calculating Ext groups over the Steenrod algebra. I wrote a MAGMA program to give the description in terms of generators (up to a given degree) of these modules over the Steenrod alegebra, in a format admissible for the program mentioned above. There is also a chart for the beginning of $\mathbf{MTSO}(2)$ with some differentials filled in here, which are those which can be deduced from John Rognes' "Two-primary algebraic K-theory of pointed spaces", Topology 41 ( PDF).