Brieskorn homology 3-spheres, GL(2,Z) and the Stern—Brocot tree
Josef Svoboda (Caltech)
| Sat Oct 24, 16:00-17:00 (starts in 29 hours) | |
| Lecture held in Temple 1169. |
Abstract: The d-invariant of a homology sphere $\Sigma(p,q,r)$ is a non-negative integer. It obstructs the existence of smooth contractible 4-manifolds with the boundary $\Sigma(p,q,r)$. By a result of Elkies, d vanishes exactly when the corresponding resolution (or plumbing) lattice is diagonalizable. We completely characterize Brieskorn spheres $Sigma(2,q,r)$ with d=0, using the combinatorics of Stern—Brocot tree and free submonoids of GL(2,Z). Joint work with Shimal Harichurn, Isabella Khan and András Némethi.
algebraic geometrycombinatorics
Audience: researchers in the discipline
Series comments: The 2026 annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place October 23-25, 2026, at VCU.
The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-2408985.
| Organizer: | Nicola Tarasca* |
| *contact for this listing |