Through the analytic halo: Fission via irregular singularities

Philip Boalch[1]

  • [1] École Normale Supérieure et CNRS 45 rue d’Ulm 75005 Paris (France)

Annales de l’institut Fourier (2009)

  • Volume: 59, Issue: 7, page 2669-2684
  • ISSN: 0373-0956

Abstract

top
This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.

How to cite

top

Boalch, Philip. "Through the analytic halo: Fission via irregular singularities." Annales de l’institut Fourier 59.7 (2009): 2669-2684. <http://eudml.org/doc/10467>.

@article{Boalch2009,
abstract = {This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.},
affiliation = {École Normale Supérieure et CNRS 45 rue d’Ulm 75005 Paris (France)},
author = {Boalch, Philip},
journal = {Annales de l’institut Fourier},
keywords = {Analytic halo; character variety; fission; moment mapping; Betti moduli space},
language = {eng},
number = {7},
pages = {2669-2684},
publisher = {Association des Annales de l’institut Fourier},
title = {Through the analytic halo: Fission via irregular singularities},
url = {http://eudml.org/doc/10467},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Boalch, Philip
TI - Through the analytic halo: Fission via irregular singularities
JO - Annales de l’institut Fourier
PY - 2009
PB - Association des Annales de l’institut Fourier
VL - 59
IS - 7
SP - 2669
EP - 2684
AB - This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic manifolds, generalising the complex character varieties of Riemann surfaces.
LA - eng
KW - Analytic halo; character variety; fission; moment mapping; Betti moduli space
UR - http://eudml.org/doc/10467
ER -

References

top
  1. Anton Alekseev, H. Burstzyn, Eckhard Meinrenken, Pure spinors on Lie groups 
  2. Anton Alekseev, Anton Malkin, Eckhard Meinrenken, Lie group valued moment maps, J. Differential Geom. 48 (1998), 445-495 Zbl0948.53045MR1638045
  3. Olivier Biquard, P. P. Boalch, Wild non-abelian Hodge theory on curves, Compos. Math. 140 (2004), 179-204 Zbl1051.53019MR2004129
  4. P. P. Boalch, Irregular connections and Kac-Moody root systems 
  5. P. P. Boalch, Stokes matrices, Poisson Lie groups and Frobenius manifolds, Invent. Math. 146 (2001), 479-506 Zbl1044.53060MR1869848
  6. P. P. Boalch, Symplectic manifolds and isomonodromic deformations, Adv. Math. 163 (2001), 137-205 Zbl1001.53059MR1864833
  7. P. P. Boalch, G -bundles, isomonodromy, and quantum Weyl groups, Int. Math. Res. Not. (2002), 1129-1166 Zbl1003.58028MR1904670
  8. P. P. Boalch, Quasi-Hamiltonian geometry of meromorphic connections, Duke Math. J. 139 (2007), 369-405 Zbl1126.53055MR2352135
  9. Pierre Deligne, Bernard Malgrange, Jean-Pierre Ramis, Singularités irrégulières, (2007), Société Mathématique de France, Paris Zbl1130.14001MR2387754
  10. N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), 59-126 Zbl0634.53045MR887284
  11. Jean Martinet, Jean-Pierre Ramis, Elementary acceleration and multisummability I, Ann. Inst. H. Poincaré Phys. Théor. 54 (1991), 331-401 Zbl0748.12005MR1128863
  12. Hiraku Nakajima, Hyper-Kähler structures on moduli spaces of parabolic Higgs bundles on Riemann surfaces, Moduli of vector bundles (Sanda, 1994; Kyoto, 1994) 179 (1996), 199-208, Dekker, New York Zbl0881.14006MR1397988
  13. Carlos T. Simpson, Harmonic bundles on noncompact curves, J. Amer. Math. Soc. 3 (1990), 713-770 Zbl0713.58012MR1040197
  14. Carlos T. Simpson, The Hodge filtration on nonabelian cohomology, Algebraic geometry—Santa Cruz 1995 62 (1997), 217-281, Amer. Math. Soc., Providence, RI Zbl0914.14003MR1492538

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.