Preprints

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.

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

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

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

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

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 Ek-algebras ( ArXiV), with Søren Galatius and Alexander Kupers.


Publications

The positive scalar curvature cobordism category ( ArXiV), with Johannes Ebert.
Duke Mathematical Journal, to appear.

Tautological rings and stabilisation ( ArXiV).
Glasgow Mathematical Journal, 64 (2022) no. 1, pp. 231-242.

An HP2-bundle over S4 with nontrivial Â-genus ( ArXiV), with Manuel Krannich and Alexander Kupers.
Comptes Rendus. Mathématique, Tome 359 (2021) no. 2, pp. 149-154.

Framings of Wg,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.

E2-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 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.

Notes on twisted Miller-Morita-Mumford classes, 2021.

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

A note on the family signature theorem, 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.

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.

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" above.)


Theses

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

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

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

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