### Preprints

**Infinite loop spaces and positive scalar curvature in the presence of a fundamental group** ( ArXiV), with Johannes Ebert.

**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* **318** (2017) 534-626.

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

*Journal of the American Mathematical Society* **31** (1) (2018) 215-268.

(This supersedes our earlier preprint arXiv:1203.6830.)

**Cohomology of automorphism groups of free groups with twisted coefficients** ( ArXiV).

*Selecta Mathematica* **24** (2) (2018) 1453-1478

(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** (pdf) ( ArXiV), with Boris Botvinnik and Johannes Ebert.

*Inventiones mathematicae* **209** (3) (2017), 749-835.

**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

**A fibre bundle of signature 4**, 2015.

**On diffeomorphisms acting on almost complex structures**, 2015.

**The complex of injective words is highly connected**, 2015.

**A combinatorial identity**, 2012.

**Non-triviality of torsion universal characteristic classes of 3-manifold bundles**, 2009.

**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).

### Adams E_{2} pages of Madsen-Tillmann spectra

Spectrum | E_{2} page | Module definition |

$\mathbf{MTO}(1)$ | Here | Here |

$\mathbf{MTO}(2)$ | Here | Here |

$\mathbf{MTSO}(2)$ | Here | Here |

$\mathbf{MTSpin}(4)$ | Here | Here |

_{2}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).