Please use this identifier to cite or link to this item:
|Scopus||Web of Science®||Altmetric|
|Title:||On the Bauer-Furuta and Seiberg-Witten invariants of families of 4-manifolds|
|Citation:||Journal of Topology, 2022; 15(2):505-586|
|Publisher:||London Mathematical Society|
|David Baraglia, Hokuto Konno|
|Abstract:||We show how the families Seiberg–Witten invariants of a family of smooth 4-manifolds can be recovered from the families Bauer–Furuta invariant via a cohomological formula. We use this formula to deduce several properties of the families Seiberg–Witten invariants. We give a formula for the Steenrod squares of the families Seiberg–Witten invariants leading to a series of mod 2 relations between these invariants and the Chern classes of the spinc index bundle of the family. As a result, we discover a new aspect of the ordinary Seiberg–Witten invariants of a 4-manifold X: they obstruct the existence of certain families of 4-manifolds with fibres diffeomorphic to X. As a concrete geometric application, we shall detect a non-smoothable family of K3 surfaces. Our formalism also leads to a simple new proof of the families wall crossing formula. Lastly, we introduce K-theoretic Seiberg–Witten invariants and give a formula expressing the Chern character of the K-theoretic Seiberg–Witten invariants in terms of the cohomological Seiberg–Witten invariants. This leads to new divisibility properties of the families Seiberg–Witten invariants.|
|Rights:||© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.|
|Appears in Collections:||Mechanical Engineering publications|
Files in This Item:
There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.