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, and stable rigidity results.
• A diffeomorphism classification of almost 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