Research Interests

 

1) Topological K- and Algebraic L-theory of C*-algebras and their relation to higher Grothendieck-Witt theory

 

2) The algebraic topology of manifolds, particularly of high dimensional ones

 

3) Algebraic K-theory

 

4) (Stable) Classification of 4-manifolds

 

 

 

Publications

 

1) The Analytical Assembly map and Index theory, J. Noncommut. Geom. 9 (2015), no. 2, 603--619. Here is the arxiv version. 

 

2) Stable Classification of 4-manifolds with 3-manifold fundamental group. J. Topol. 10, (2017), no. 3, 827--881. This is joint with Daniel Kasprowski, Peter Teichner and Mark Powell. Here is the arxiv version.

 

3) Localization of Cofibration categories and groupoid C*-algebras. Algebr. Geom. Topol. 17 (2017), no. 5, 3007--3020. This is joint with Thomas Nikolaus and Karol Szumiło. Here is the arxiv version.

 

4) On the relation between K- and L-theory of C*-algebras. Math. Ann. 371 (2018), no. 1-2, 517--563. This is joint with Thomas Nikolaus. Here is the arxiv version.

 

5) On the K-theory of pullbacks. Ann. of Math. (2) 190 (2019), no. 3, 877--930. This is joint with Georg Tamme. Here is the arxiv version. 

 

6) A Vanishing theorem for tautological classes of aspherical manifolds. Geometry & Topology 25-1 (2021), 47--110. This is joint with Fabian Hebestreit, Wolfgang Lück and Oscar Randal-Williams. Here is the arxiv version. 

 

7) On the homotopy type of L-spectra of the integers. J. Topol. 14, (2021), no. 1, 183--214. This is joint with Fabian Hebestreit and Thomas Nikolaus. Here is the arxiv version. The published version contains an erroneous (but for the paper irrelevant) remark in the appendix. Here you can find a corrected version of said remark.

 

8) Topological 4-manifolds with 4-dimensional fundamental group. Accepted for publication at Glasgow Math. J. This is joint with Daniel Kasprowski. Here is the arxiv version.

Preprints

 

9) Reducibility of low dimensional Poincaré duality spaces. Here is the arxiv version. WARNING: The current version contains an error: Lemma 3.2 is wrong. The main theorem is valid as stated. An update will appear soon. Apologies for the long delay!

 

10) Connected sum decompositions of high-dimensional manifolds. This is joint with Imre Bokor, Diarmuid Crowley, Stefan Friedl, Fabian Hebestreit, Daniel Kasprowski, and Johnny Nicholson. Here is the arxiv version.

 

11) Topologically flat embedded 2-spheres in specific simply connected 4-manifolds. This is joint with Daniel Kasprowski, Peter Lambert-Cole and Ana G. Lecuona. Here is the arxiv version.

 

12) Purity in chromatically localized algebraic K-theory. This replaces a previous version (``Vanishing results for chromatic localizations of algebraic K-theory'') and is now joint with Akhil Mathew, Lennart Meier, and Georg Tamme. Here is the arxiv version.

 

13) Hermitian K-theory for stable infinity-categories I: Foundations. This is joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Here is the arxiv version.

 

14) Hermitian K-theory for stable infinity-categories II: Cobordism categories and additivity. This is joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Here is the arxiv version.

 

15) Hermitian K-theory for stable infinity-categories III: Grothendieck-Witt groups of rings. This is joint with Baptiste Calmès, Emanuele Dotto, Yonatan Harpaz, Fabian Hebestreit, Kristian Moi, Denis Nardin, Thomas Nikolaus, and Wolfgang Steimle. Here is the arxiv version.

 

16) A stable $\infty$-category for equivariant KK-theory. This is joint with Ulrich Bunke and Alexander Engel. Here is the arxiv version.

 

17) Paschke duality and assembly maps. This is joint with Ulrich Bunke and Alexander Engel. Here is the arxiv version.

 

 

Book

 

18) Introduction to Infinity-categories. Compact Textbooks in mathematics, Birkhäuser, Cham, 2021. Here is the official webpage for the book with Springer.