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The quasi fibered boundary (QFB) compactification of monopole moduli spaces

Banff International Research Station for Mathematical Innovation and Discovery

The moduli spaces $M_k$ of $SU(2)$ monopoles on $R^3$ of charge $k$ are among the oldest studied objects in gauge theory, yet open questions still remain, such as Sen's conjecture for their $L^2$ cohomology. I will discuss compactifications of these moduli spaces as manifolds with corners, with respect to which their hyperKahler metrics are of "quasi fibered boundary" (QFB) type, a metric structure which generalizes the quasi asymptotically locally euclidean (QALE) and quasi asymptotically conic (QAC) structures introduced by Joyce and others. This geometric structure, which is best understood by comparison to the simpler moduli space of point clusters on $R^3$, systematically organizes the various asymptotic regions of the moduli space in which charge $k$ monopoles decompose into widely separated monopoles of charges summing to $k$. This is joint work with M. Singer and K. Fritzsch.

Mathematics; Algebraic Geometry; Differential Geometry

video/mp4

Author affiliation: New College of Florida

2021-08-03

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/79176

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/