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. 

Preprints

 

6) A Vanishing theorem for tautological classes of aspherical manifolds. This is joint with Fabian Hebestreit, Wolfgang Lück and Oscar Randal-Williams. Here is the arxiv version. Submitted for publication.

 

7) Reducibility of low dimensional Poincaré duality spaces. Here is the arxiv version. 

 

8) 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.

 

9) 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.