Nicht eingeloggt (Login)

PQLHT | Conference Talk 2 by Marco Marengon: "A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds"

Leertaste = Abspielen/Pausieren
m = Stumm
f = Vollbild
Pfeil-links = Zurückspulen
Pfeil-rechts = Vorspulen
Lukas Lewark

PQLHT | Conference Talk 2 by Marco Marengon: "A generalization of Rasmussen's invariant, with applications to surfaces in some four-manifolds"

We extend the definition of Khovanov-Lee homology to links in connected sums of S1×S2, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in S1×S2, we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussen-type invariant to the genus of surfaces with boundary in the following four-manifolds: B2×S2, S1×B3, CP2, and various connected sums and boundary sums of these. We deduce that Rasmussen's invariant also gives genus bounds for surfaces inside homotopy four-balls obtained from B4 by a certain operation called Gluck twists. Therefore, Rasmussen’s invariant cannot be used to prove that such homotopy four-balls are non-standard.

This talk was part of the conference "Perspectives on quantum link homology theories", see https://cbz20.raspberryip.com/Perspectives-2021

Sprungmarken