LdT Seminar Tomorrow (Bais).

[Rafael Torres]

 Speaker: Valentina Bais (SISSA)

Title: Some examples of small exotic 4-manifolds with free abelian fundamental group

Abstract: In a joint work with Rafael Torres and Daniele Zuddas, we pin down the homeomorphism type of some closed oriented 4-manifolds with free abelian fundamental group. Such examples come in infinite families and are produced via torus-surgery-based constructions from some closed non-simply-connected 4-manifolds with small Euler characteristics appearing in the work of Akhmedov-Park, Baldridge-Kirk and Torres. The diffeomorphism types are distinguished by the Seiberg-Witten invariants and any two homeomorphic 4-manifolds in these collections become diffeomorphic after connected summing with a single copy of a product of two 2-spheres. In this talk, I will explain the notion of equivariant intersection form of a closed oriented 4-manifolds and I will sketch the main ideas beyond the computation of this invariant for the examples in our main result. This algebraic tool is indeed the main ingredient for understanding the homeomorphism type of closed oriented 4-manifolds with fundamental group Z and Z^2, as implied by classification results by Freedman-Quinn, Stong-Wang and Hambleton-Kreck-Teichner.

Date: Thursday March 27th, 2025
Time: 11:00 am
Venue: Room 136