8 citations · 35 across the 18 of their papers we have counts for
13 papers · 1 filter
Analytic convergence of harmonic metrics for parabolic Higgs bundles
Semin Kim, Graeme Wilkin
In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric de…
Conditions of smoothness of moduli spaces of flat connections and of character varieties
Nan-Kuo Ho, Graeme Wilkin, Siye Wu
We use gauge theoretic and algebraic methods to examine sufficient conditions for smooth points on the moduli space of flat connections on a compact manifold and on the character v…
Higgs bundles over cell complexes and representations of finitely generated groups
George Daskalopoulos, Chikako Mese, Graeme Wilkin
The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle…
The reverse Yang-Mills-Higgs flow in a neighbourhood of a critical point
Graeme Wilkin
The main result of this paper is a construction of solutions to the reverse Yang-Mills-Higgs flow converging in the topology to a critical point. The construction uses o…
Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes
Indranil Biswas, Graeme Wilkin
We study complex Lagrangian submanifolds of a compact hyper-Kähler manifold and prove two results: (a) that an involution of a hyper-Kähler manifold which is antiholomorphic with r…
Morse Theory, Higgs fields and Yang-Mills-Higgs functionals
Steven Bradlow, Graeme Wilkin
In this paper we give an overview of different Morse-theoretic methods used to study the topology of moduli spaces of Higgs bundles.