Research

• MathSciNet reviews • Zentralblatt reviews • arXiv postings •

Submitted/posted papers

with Sebastian Goette and Thorsten Hertl : Path components of G₂-moduli spaces may be non-aspherical. arXiv:2503.15829
with Mark Grant : Immersed but not embedded homology classes. arXiv:2412:15359
with Csaba Nagy : The Witt groups of extended quadratic forms over Z. arXiv:2404.09189
with Huijun Yang : The existence of contact structures on 9-manifolds. arXiv:2011.09809
with Xing Gu and Christian Haesemeyer : On The Topological Period-Index Problem over 8-manifolds. arXiv:1911.07206

Announcement

with Csaba Nagy : Inertia groups of 3-connected 8-manifolds, Melbourne 2019

Accepted papers

with Xing Gu : On H^*(BPU_n; ℤ) and Weyl group invariants. To appear in Trans. Amer. Math. Soc.. arXiv:2103.03523
with Anthony Conway, Mark Powell and Joerg Sixt : Stably diffeomorphic manifolds and modified surgery obstructions. To appear in Mem. Soc. Math. France.. arXiv:2109:05632

Published papers and book chapter

with Sebastian Goette and Johannes Nordström : An analytic invariant of G₂-manifolds, Invent. Math. 239 (2025), 865–907. arXiv:1505.02734
with Csaba Nagy : The smooth classification of 4-dimensional complete intersections, Geom. Topol. 29 (2025), 269–311. arXiv:2003.09216
with Csaba Nagy, Blake Sims and Huijun Yang : Turning vector bundles, Algebr. Geom. Topol. 24 (2024), 2807–2849. arXiv:2204.08678
with Thomas Schick and Wolfgang Steimle : The derivative map for diffeomorphisms of discs: An example, Geom. Topol. 27 (2023), 3699–3713. arXiv20.12.13634
with Anthony Conway and Mark Powell : Infinite homotopy stable class for 4-manifolds with boundary, Pacific J. Math. 325 (2023), 209–237. arXiv:2210.00927
with Anthony Conway, Mark Powell and Joerg Sixt : Simply-connected manifolds with large homotopy stable classes, J. Aust. Math. Soc. 115 (2023), 172–203. arXiv:2109:00654
with Jonathan Bowden : Contact open books with flexible pages, Bull. Lond. Math. Soc. 55 (2023), 1302–1313. arXiv:2106.06253
with David Wraith : Intermediate curvatures and highly connected manifolds, AJM 26 (2022), 407–454. arXiv:1704.07057
with Arkadiy Skopenkov : Embeddings of non-simply-connected 4-manifolds in 7-space. II. On the smooth classification, Proc. Roy. Soc. Edinburgh Sect. A (2022), 163–181. arXiv1612.04776
with Johannes Nordström : Exotic G₂-manifolds, Math. Ann. 381 (2021), 29–74. arXiv:1411.0656
with Imre Bokor, Stefan Friedl, Fabian Hebestreit, Markus Land, Daniel Kasprowski and Johnny Nicholson : Connected sum decompositions of high-dimensional manifolds. 2019-20 MATRIX Annals. arXiv:1909.02628
with Arkadiy Skopenkov : Embeddings of non-simply-connected 4-manifolds in 7-space. I. Classification modulo knots, Mosc. Math. J. 21 (2021), 43–98. arXiv1611.04738
with Sebastian Goette and Johannes Nordström : Distinguishing G₂-manifolds, Lectures and Surveys on G₂-manifolds and Related Topics, Springer 2020, 143–172: Edited by Spiro Karigiannis, Conan Nai Chung Leung and Jason Lotay. arXiv:1808.05585
with Mark Grant : The Topological Period-Index Problem for spin^c 6-manifolds, Ann. K-Theory 5 (2020), 605–620. arXiv:1802.01296
with Johannes Nordström : The rational homotopy type of (n-1)-connected manifolds of dimension up to 5n-3, J. Topol. 13 (2020), 539–575. arXiv:1505.04184
with Tibor Macko : On the cardinality of the manifold set, Geom. Dedicata 200 (2019), 265–285. arXiv:1708.02089
with Johannes Nordström : The classification of 2-connected 7-manifolds, Proc. London Math. Soc. 119 (2019), 1–54. arXiv:1406.2226
with Thomas Schick and Wolfgang Steimle : Harmonic spinors and metrics of positive scalar curvature via the Gromoll filtration and Toda brackets, J. Topol. 11 (2018), 1076–1098. arXiv1612.04660
with David Wraith : Positive Ricci curvature on highly connected manifolds, J. Diff. Geom. 106 (2017), 187–243. arXiv:1404.7446
with Mark Grant : The Poincaré-Hopf Theorem for line fields revisited, J.G.P. 117 (2017), 187–196. arXiv:1612.04073
with Jonathan Bowden and András Stipsicz : The topology of Stein fillable manifolds in high dimensions II, Geom. Topol. 19 (2015), 2995–3030. arXiv:1409.7504
with Johannes Nordström : A new invariant of G₂-structures, Geom. Topol. 19 (2015), 2949–2992. arXiv:1211.0269
with Ian Hambleton : Finite group actions on Kervaire manifolds, Adv. Math. 283 (2015), 88–129. arXiv:1305.6546
with Clara Löh : Functorial semi-norms on singular homology and (in)flexible manifolds, Algebr. Geom. Topol. 15 (2015), 1453–1499. arXiv:1103.4139
with Jonathan Bowden and András Stipsicz : The topology of Stein fillable manifolds in high dimensions I, Proc. Lond. Math. Soc. 109 (2014), 1363–1401. arXiv:1306.2746
with Jonathan Bowden and András Stipsicz : Contact structures on M x S², Math. Ann. 358 (2014), 351–359. arXiv:1305.3121
with Steve Ferry and Mikhail Skopenkov : The rational classification of links of codimension > 2, Forum Math. 26 (2014), 239–269. arXiv1106.145
with Thomas Schick : The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature, Geom. Topol. 17 (2013), 1773–1789. arXiv1204.6474
with Sebastian Goette : Kreck-Stolz invariants for quaternionic line bundles, Trans. Amer. Math. Soc. 365 (2013), 3193–3225. arXiv:1012.5237
On the mapping class groups of #_r(S^p x S^p) for p = 3, 7, Math. Zeit. 269 (2011), 1189–1199. arXiv:0905.0423
with Joerg Sixt : Stably diffeomorphic manifolds and l_2q+1(Z[π]), Forum Math. 23 (2011), 483–538. arXiv:0808.2008
with Arkadiy Skopenkov : A Classification of Smooth Embeddings of 4-manifolds in 7-space II, Internat. J. Math. 22 (2011), 731–757. arXiv:0808.1795
with Tibor Macko : The additivity of the \rho-invariant and periodicity in topological surgery, Algebr. Geom. Topol. 11 (2011), 1915–1959. arXiv:1002.1917
The smooth structure set of S^p x S^q, Geom. Dedicata 148 (2010), 15–33. arXiv:0904.1370
with Peter Zvengrowski : On the non-invariance of span and immersion co-dimension for manifolds, Arch. Math. (Brno) 44 (2008), 353–365.
with Christine Escher : A classification of S³-bundles over S⁴, Differential. Geom. Appl. 18 (2003), 363–380. arXiv:0004147
with Alan Carey and Michael Murray : Principle bundles and the Dixmier Duoady class, Comm. Math. Phys. 193 (1998), 171–196. arXiv:9702147

Book contribution

Surgery Theory: Foundations by Wolfgang Lück and Tibor Macko

Problem list

with Jonathan Bowden, Jim Davis, Stefan Friedl, Carmen Rovi and Stephan Tillmann : Open Problems in the Topology of Manifolds, MATRIX Annals 2019-20, 647--659.

Surveys and definition

with Matthias Kreck : Hirzebruch surfaces, Bull. Man. Atl. (2011).
5-manifolds: 1-connected, Bull. Man. Atl. (2011).
with Matthias Kreck : Microbundle, Bull. Man. Atl. (2013).

Dissertation: Indiana University 2002

On the classification of highly connected manifolds in dimensions 7 and 15, Bloomington, Indiana (2002). arXiv:0203253 - Corrections at the Manifold Atlas

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