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pro vyhledávání: '"Bradlow, Steven"'
Autor:
Bradlow, Steven
The moduli spaces for Higgs bundles associated to real Lie groups and a closed Riemann surface have multiple connected components. This survey provides a compendium of results concerning the counting of these components in cases where the Lie group i
Externí odkaz:
http://arxiv.org/abs/2312.00762
Publikováno v:
Internat. J. Math. 32 (2021), no. 13, Paper No. 2150096, 19 pp
Given a compact Riemann surface $\Sigma$ of genus $g_\Sigma\, \geq\, 2$, and an effective divisor $D\, =\, \sum_i n_i x_i$ on $\Sigma$ with $\text{degree}(D)\, <\, 2(g_\Sigma -1)$, there is a unique cone metric on $\Sigma$ of constant negative curvat
Externí odkaz:
http://arxiv.org/abs/2101.03080
Akademický článek
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Publikováno v:
Communications in Analysis and Geometry Volume 28, Number 8, 2020
We examine Higgs bundles for non-compact real forms of SO(4,C) and the isogenous complex group SL(2,C)XSL(2,C). This involves a study of non-regular fibers in the corresponding Hitchin fibrations and provides interesting examples of non-abelian spect
Externí odkaz:
http://arxiv.org/abs/1909.03994
Autor:
Aparicio-Arroyo, Marta, Bradlow, Steven, Collier, Brian, García-Prada, Oscar, Gothen, Peter, Oliveira, André
Publikováno v:
Inventiones Mathematicae, 218 (2019), 197-299
Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by p
Externí odkaz:
http://arxiv.org/abs/1802.08093
Autor:
Aparicio-Arroyo, Marta, Bradlow, Steven, Collier, Brian, Garcia-Prada, Oscar, Gothen, Peter, Oliveira, André
Publikováno v:
C. R. Acad. Sci. Paris, Ser. I, 356 (2018), 666-673
For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. In many cases, natural topological invariants label connected components of the moduli spaces. Hi
Externí odkaz:
http://arxiv.org/abs/1801.08561
We propose a method for demonstrating sub community structure in scientific networks of relatively small size from analyzing databases of publications. Research relationships between the network members can be visualized as a graph with vertices corr
Externí odkaz:
http://arxiv.org/abs/1705.01591
Publikováno v:
Geometry and Physics: Volume 2, A Festschrift in honour of Nigel Hitchin, Oxford University Press, 2018, pp. 455-470
We give necessary and sufficient conditions for moduli spaces of semistable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotent cone of GL_n-Higgs bundles and the irreducible compon
Externí odkaz:
http://arxiv.org/abs/1703.06168
Publikováno v:
Research in the Mathematical Sciences 2016 3:14
We explore relations between Higgs bundles that result from isogenies between low-dimensional Lie groups, with special attention to the spectral data for the Higgs bundles. We focus on isogenies onto $SO(4,C)$ and $SO(6,C)$ and their split real forms
Externí odkaz:
http://arxiv.org/abs/1508.02650
Autor:
Bradlow, Steven, Wilkin, Graeme
In this paper we give an overview of different Morse-theoretic methods used to study the topology of moduli spaces of Higgs bundles.
Comment: 38 pages, J. Fixed Point Theory Appl. 11 (2012), no. 1
Comment: 38 pages, J. Fixed Point Theory Appl. 11 (2012), no. 1
Externí odkaz:
http://arxiv.org/abs/1308.1460