### Preprints

**The Alexander trick for homology spheres** ( ArXiV), with Søren Galatius.

**Monodromy and mapping class groups of 3-dimensional hypersurfaces** ( ArXiV).

**Configuration spaces as commutative monoids** ( ArXiV), with an appendix with Quoc P. Ho.

**Stable cohomology of congruence subgroups** ( ArXiV).

Appendix to **
Asymptotic mapping class groups of Cantor manifolds and their finiteness properties** ( ArXiV), by Javier Aramayona, Kai-Uwe Bux, Jonas Flechsig, Nansen Petrosyan, Xiaolei Wu.

**
Diffeomorphisms of discs and the second Weiss derivative of BTop(-)** ( ArXiV), with Manuel Krannich.

**Quantization of Chern-Simons topological invariants for H-type and L-type quantum systems** ( ArXiV), with Lokman Tsui and Xiao-Gang Wen.

**On diffeomorphisms of even-dimensional discs** ( ArXiV), with Alexander Kupers.

**E _{∞}-cells and general linear groups of infinite fields** ( ArXiV), with Søren Galatius and Alexander Kupers.

**E _{∞}-cells and general linear groups of finite fields** ( ArXiV), with Søren Galatius and Alexander Kupers.

**Cellular E _{k}-algebras** ( ArXiV), with Søren Galatius and Alexander Kupers.

### Publications

**Differential cohomology and topological actions in physics** ( ArXiV), with Joe Davighi and Ben Gripaios.

*Advances in Theoretical and Mathematical Physics*, to appear.

**Algebraic independence of topological Pontryagin classes** ( ArXiV), with Søren Galatius.

*Journal für die reine und angewandte Mathematik*, to appear.

**On the cohomology of Torelli groups. II** ( ArXiV).

*International Mathematics Research Notices*, to appear.

**Generalized symmetries of topological field theories** ( ArXiV), with Ben Gripaios and Joseph Tooby-Smith.

*Journal of High Energy Physics*, **2023** No. 3 (2023), E87.

**On the Torelli Lie algebra** ( ArXiV), with Alexander Kupers.

*Forum of Mathematics, Pi*, **11** (2023) E13.

**The family signature theorem** ( ArXiV).

*Proceedings of the Royal Society of Edinburgh* (Ranicki memorial issue), to appear.

**Classical homological stability from the point of view of cells** ( ArXiV).

*Algebraic & Geometric Topology*, to appear.

**On automorphisms of high-dimensional solid tori** ( ArXiV), with Mauricio Bustamante.

*Geometry & Topology*, to appear.

**On the order of Dehn twists** ( ArXiV), with Ailsa Keating.

*New York Journal of Mathematics*, **29** (2023), pp. 203-212.

**
Diffeomorphisms of discs** ( ArXiV).

To appear in the Proceedings of the ICM, 2022.

**The positive scalar curvature cobordism category** ( ArXiV), with Johannes Ebert.

*Duke Mathematical Journal*, **171** (11) (2022), pp. 2275-2406.

**Tautological rings and stabilisation** ( ArXiV).

*Glasgow Mathematical Journal*, **64** (2022) no. 1, pp. 231-242.

**An HP ^{2}-bundle over S^{4} with nontrivial Â-genus** ( ArXiV), with Manuel Krannich and Alexander Kupers.

*Comptes Rendus. Mathématique*, Tome

**359**(2021) no. 2, pp. 149-154.

**Framings of W _{g,1}** ( ArXiV), with Alexander Kupers.

*Quarterly Journal of Mathematics*,

**72**(2021) no. 3, pp. 1029-1053.

**Homology of Hurwitz spaces and the Cohen--Lenstra heuristic for function fields (after Ellenberg, Venkatesh, and Westerland)** ( ArXiV).

*Astérisque* No. **422** Séminaire Bourbaki, volume 2018/2019, exposés 1151-1165 (2020), Exp. No. 1164,469-497.

**The cohomology of Torelli groups is algebraic** ( ArXiV), with Alexander Kupers.

*Forum of Mathematics, Sigma*, **8** (2020), E64.

**Mapping class groups of simply connected high-dimensional manifolds need not be arithmetic** ( ArXiV), with Manuel Krannich.

*Comptes Rendus. Mathématique*, Tome **358** (2020) no. 4, pp. 469-473.

**Operations on stable moduli spaces** ( ArXiV), with Søren Galatius.

*Research in the Mathematical Sciences*, **7** (2020), E9.

**On the cohomology of Torelli groups** ( ArXiV), with Alexander Kupers.

*Forum of Mathematics, Pi*, **8** (2020), E7.

Erratum

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

*Geometry & Topology* **25** (2021), 47-110.

**Moduli spaces of manifolds: a user's guide** ( ArXiV), with Søren Galatius.

Chapter for *Handbook of Homotopy Theory*.

**E _{2}-cells and mapping class groups** ( ArXiV), with Søren Galatius and Alexander Kupers.

*Institut des Hautes Études Scientifiques. Publications Mathématiques*,

**130**(1) (2019) 1-61.

**Semisimplicial spaces** ( ArXiV), with Johannes Ebert.

*Algebraic & Geometric Topology* **19** (4) (2019) 2099-2150.

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

*Geometry & Topology* **23** (2019) 1549-1610.

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

*Physics Letters B* **782** (2018) 94-98.

**Some phenomena in tautological rings of manifolds** ( ArXiV).

*Selecta Mathematica* **24** (4) (2018) 3835-3873.

**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* (Quillen Memorial Issue) **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 remark on the homology of Temperley--Lieb algebras**, 2021.

**Miller-Morita-Mumford classes vanish on the moduli space of hypersurfaces**, 2019.

**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.

**Algebraic independence of topological Pontrjagin classes**, for the "Topologie" Oberwolfach report, 2022.

**On Rognes' connectivity conjecture**, for the "Topologie" Oberwolfach report, 2018.

**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.

**A note on the family signature theorem**, 2019. (Superseded by "The family signature theorem".)

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

**The stable cohomology of automorphisms of free groups with coefficients in the homology representation** ( ArXiV). (Superseded by "Cohomology of automorphism groups of free groups with twisted coefficients".)

### Theses

Ismael Sierra, Homological stability of spaces of manifolds via E_{k}-algebras, University of Cambridge, 2023.

Andreas Stavrou, Homology of Configuration Spaces of Surfaces as Mapping Class Group Representations, University of Cambridge, 2023.

Nils Prigge, On tautological classes of fibre bundles and self-embedding calculus, University of Cambridge, 2020.

Nina Friedrich, Automorphism Groups of Quadratic Modules and Manifolds, University of Cambridge, 2017.

Mauricio Gómez López, Spaces of piecewise linear manifolds, University of Copenhagen, 2014.

Federico Cantero Morán, Homology Stability for Spaces of Surfaces, Universitat de Barcelona, 2013.