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Seminar

Diffeomorphisms and Gauge Theory Seminar: Family Seiberg-Witten invariant and nonsymplectic loops of diffeomorphisms September 30, 2022 (09:30 AM PDT - 10:30 AM PDT)
Parent Program:
Location: MSRI: Simons Auditorium, Online/Virtual
Speaker(s) Jianfeng Lin (Tsinghua University)
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Diffeomorphisms And Gauge Theory Seminar: Family Seiberg-Witten Invariant And Nonsymplectic Loops Of Diffeomorphisms

Abstract/Media

To participate in this seminar, please register HERE.

By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. When the cutting 3-manifold is an L-space, this formula implies a relation between the family Seiberg-Witten invariant, the Seiberg-Witten invariant of the fiber and the index of the family Dirac operator. We use this relation to calculate the Seiberg-Witten invariant of families of 4-manifolds that arise when resolving an ADE singularity using a hyperkähler family of complex structures near the singularity.  Applications include a Z^\infty summand in the fundamental group of Diff(M) for many simply connected 4-manifolds.

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Diffeomorphisms And Gauge Theory Seminar: Family Seiberg-Witten Invariant And Nonsymplectic Loops Of Diffeomorphisms