### Invariants of rational homology 3-spheres from the abelianization of the mod-p Torelli group (Virtual)

- Series
- Geometry Topology Seminar
- Time
- Monday, October 4, 2021 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Ricard Riba Garcia – UAB Barcelona – riba@mat.uab.cat

Unlike the integral case, given a prime number p, not all Z/p-homology 3-spheres can be constructed as a Heegaard splitting with a gluing map an element of mod p Torelli group, M[p]. Nevertheless, letting p vary we can get any rational homology 3-sphere. This motivated us to study invariants of rational homology 3-spheres that comes from M[p]. In this talk we present an algebraic tool to construct invariants of rational homology 3-spheres from a family of 2-cocycles on M[p]. Then we apply this tool to give all possible invariants that are induced by a lift to M[p] of a family of 2-cocycles on the abelianization of M[p], getting a family of invariants that we will describe precisely.