5/ As an application, they compute indices for large surgeries, confirming conjectures and revealing new structural patterns.The results suggest a well-defined extension of the index to closed manifolds.

4/ Building on a reinterpretation of the index as a generating function over Q-normal surfaces, the authors develop a gluing formula for relative indices.

2/ The paper proves the Gang–Yonekura formula, describing how the 3D index transforms under Dehn filling a cusp in a 3-manifold.

Excited about this one: seminargeotop-a.com/next-talks
Speaking in a few hours (7am Los Angeles/10am NY/3pm Paris and midnight QLD) about a joint work with @aklotz.bsky.social and Dimos Goundaroulis!

Topological features also identify locations of mutations that are disease-causing and structurally damaging, and capture differences between homologous enzymes in thermophile and mesophile organisms.

We analyze topologically the whole of AlphaFold2, and show how topological features capture global features of the protein universe, such as domain architecture, binding sites and thermodynamics.

New preprint "The Topological Properties of the Protein Universe". Work carried on by PhD student Christian Madsen, with @syz.bsky.social, M. Stumpf, D. Pires and others www.biorxiv.org/content/10.1...