Homological Stability for Asymptotic Monopole Moduli Spaces
Event details
Date | 31.05.2022 |
Hour | 10:15 › 11:15 |
Speaker | Martin Palmer, Institutul de Matematică Simion Stoilow al Academiei Române |
Location | |
Category | Conferences - Seminars |
Event Language | English |
Magnetic monopoles were introduced by Dirac in 1931 to explain the quantisation of electric charges. In his model, they are singular solutions to an extension of Maxwell's equations allowing non-zero magnetic charges. An alternative model, developed by 't Hooft and Polyakov in the 1970s, is given (after a certain simplification) by smooth solutions to a different set of equations, the Bogomolny equations, whose moduli space of solutions has connected components M_k indexed by positive integers k. These have been intensively studied, notably by Segal (stabilisation of their homotopy groups) and Cohen-Cohen-Mann-Milgram (describing their stable homotopy types in terms of braid groups).
A compactification of M_k has recently been proposed by Fritzsch-Kottke-Singer, whose boundary strata we call asymptotic monopole moduli spaces. I will describe ongoing joint work with Ulrike Tillmann in which we study stability patterns in the homology of these spaces.
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