Title: The Obstruction of Orientability of Real Monopole Floer Homology

Abstract: The Real Seiberg-Witten theory is one of a stong tool in knot theory and surface knot theory. For example, that can detect exotic P^2-knot and Kang-Park-Taniguchi proved that any non trivial cable of figure eight knot is not slice using Real Seiberg-Witten theory. This theory is also provide interesting phenomena in index theory, since Real Seiberg-Witten theory can be seen as a "non-linear version" of Atiya's Real K-theory. For example, there is an obstruction to orient moduli space of Real Seiberg-Witten eqations on closed 4-manifolds. Recently, Bonciocat obtained a obstruction to lift the real Heegaard Floer homology from mod 2 coefficient to Z-coefficient. In this talk, we give a canonical way to obtain Z- coefficient real monopole Floer homology of double branced cover of a link in homology S^3 in the case when the obstruction vanishes. We also proved that the Bonciocat's obstruction is also obstract Z-coefficient in real monopole, however the proof is different. This is joint work with Jiakai Li.

Speaker: Jin Miyazawa (RIMS, Kyoto University)

This talk will also be broadcast online via Zoom: 
Meeting ID: 974 4775 6289
Passcode: 371131

Language: English

This lecture is part of the  Thematic Program on “New Frontiers in Gauge Theory, Topology, and Physics” (TP26GT).