Homepage of Maximilian Hans

I am a PhD student of Daniel Kasprowski at the University of Southampton. Before that, I was based in Bonn, working with Peter Teichner. My research interests lie primarily at the intersection of geometric topology and homotopy theory. This includes spaces of embeddings and diffeomorphisms, 4-manifolds, surgery theory, K- and L-Theory, and cobordism categories.

Articles:

• A note on Duality and the Atiyah–Hirzebruch spectral sequence (arXiv), to appear in Glasgow Mathematical Journal

Projects:

• A bridge between classical and modified surgery: I investigate a direct comparison between classical and modified surgery theory, to compare equivalence relations (homotopy equivalence, stable homeomorphism, and homeomorphism) on manifolds. This includes rigidity, stable rigidity results, as well as cancellation results.
• Group actions on highly connected manifolds: In joint work with Oleksandr Kharchenko, we are working on a diffeomorphism classification of even-dimensional manifolds whose universal covering is highly connected, while a non-trivial fundamental group is present.

Here are some notes I have written covering various topics.

• Poincaré categories.
• A Light Bulb Theorem for Multi-Disks.
• The Kervaire Invariant and a non-smoothable Manifold.
• The Pontrjagin–Thom Construction.
• The Birman–Craggs Homomorphisms.
• Symplectic Representation of the Mapping Class Group.

Contact: maximilian.hans(at)soton.ac.uk
Office: Room 8035, B54, West Highfield Campus, University Road, SO17 1BJ