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Constraints on Lefschetz fibrations with four-dimensional fibers from Seiberg-Witten theory
Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee +1
We establish constraints on the topology of smooth Lefschetz fibrations with -dimensional fibers, by studying the family Bauer-Furuta invariant. To compute this invariant, we an…
The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory
Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee +1
We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class…
On four-dimensional Dehn twists and Milnor fibrations
Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee +1
We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twis…
Corks for exotic diffeomorphisms
Vyacheslav Krushkal, Anubhav Mukherjee, Mark Powell +1
We prove a localization theorem for exotic diffeomorphisms, showing that every diffeomorphism of a compact simply-connected 4-manifold that is isotopic to the identity after stabil…
Existence and construction of non-loose knots
Rima Chatterjee, John B. Etnyre, Hyunki Min +1
In this paper we give necessary and sufficient conditions for a knot type to admit non-loose Legendrian and transverse representatives in some overtwisted contact structure, classi…
One stabilization is not enough for closed knotted surfaces
Kyle Hayden, Sungkyung Kang, Anubhav Mukherjee
In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either exter…