|Location:||MSRI: Simons Auditorium, Online/Virtual|
Diffeomorphisms And Gauge Theory Seminar: Family Seiberg-Witten Invariant And Nonsymplectic Loops Of Diffeomorphisms
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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.No Notes/Supplements Uploaded