Twisted character varieties, covering spaces, and gerbes
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 471-494 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a finite-index subgroup $\widetilde\Pi$ of a finitely generated group $\Pi$, we establish various relations between (twisted) character varieties of $\Pi$ and $\widetilde\Pi$. We interpret our results geometrically in terms of the moduli space of flat connections on principal bundles twisted by a flat bundle gerbe over a manifold with the fundamental group $\Pi$.
Mots-clés : moduli space, gerbe
Keywords: character variety, twisted bundle.
@article{TMF_2015_185_3_a5,
     author = {S. Wu},
     title = {Twisted character varieties, covering spaces, and gerbes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {471--494},
     year = {2015},
     volume = {185},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a5/}
}
TY  - JOUR
AU  - S. Wu
TI  - Twisted character varieties, covering spaces, and gerbes
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2015
SP  - 471
EP  - 494
VL  - 185
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a5/
LA  - ru
ID  - TMF_2015_185_3_a5
ER  - 
%0 Journal Article
%A S. Wu
%T Twisted character varieties, covering spaces, and gerbes
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2015
%P 471-494
%V 185
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a5/
%G ru
%F TMF_2015_185_3_a5
S. Wu. Twisted character varieties, covering spaces, and gerbes. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 471-494. http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a5/

[1] M. S. Narasimhan, C. S. Seshadri, Ann. Math., 82:3 (1965), 540–567 | DOI | MR | Zbl

[2] M. F. Atiyah, R. Bott, Philos. Trans. Roy. Soc. London Ser. A, 308:1505 (1983), 523–615 | DOI | MR | Zbl

[3] E. Witten, Commun. Math. Phys., 141:1 (1991), 153–209 | DOI | MR | Zbl

[4] N.-K. Ho, Int. Math. Res. Notices, 2004:61 (2004), 3263–3285, arXiv: math.SG/0312426 | DOI | MR | Zbl

[5] N.-K. Ho, C.-C. M. Liu, Int. Math. Res. Notices, 2003:44 (2003), 2359–2371, arXiv: math.SG/0303255 | DOI | MR

[6] N.-K. Ho, C.-C. M. Liu, Commun. Anal. Geom., 16:3 (2008), 617–679, arXiv: math.SG/0605587 | DOI | MR | Zbl

[7] N.-K. Ho, C.-C. M. Liu, D. A. Ramras, Commun. Anal. Geom., 17:5 (2009), 903–953, arXiv: 0810.4882 | DOI | MR | Zbl

[8] T. J. Baird, Q. J. Math., 61:2 (2010), 141–170, arXiv: 0806.1975 | DOI | MR | Zbl

[9] F. Schaffhauser, Geom. Dedicata, 151 (2011), 187–206, arXiv: 0912.0659 | DOI | MR | Zbl

[10] N.-K. Ho, G. Wilkin, S. Wu, Hitchin's equations on a nonorientable manifold, arXiv: 1211.0746

[11] T. Hausel, F. Rodriguez-Villegas, Invent. Math., 174:3 (2008), 555–624, arXiv: math.AG/0612668 | DOI | MR | Zbl

[12] M. A. A. de Cataldo, T. Hausel, L. Migliorini, Ann. Math., 175:3 (2012), 1329–1407, arXiv: 1004.1420 | DOI | MR | Zbl

[13] M. Mulase, “Geometry of character varieties of surface groups”, Geometry Related to the Theory of Integrable Systems, RIMS Kôkyûroku, 1605, ed. R. Miyaoka, RIMS, Kyoto, 2008, 1–21, arXiv: 0710.5263

[14] M. K. Murray, J. London Math. Soc., 54:2 (1996), 403–416, arXiv: dg-ga/9407015 | DOI | MR | Zbl

[15] A. Kapustin, Adv. Theor. Math. Phys., 4:1 (2000), 127–154, arXiv: hep-th/9909089 | DOI | MR | Zbl

[16] P. Bouwknegt, V. Mathai, JHEP, 03 (2000), 007, 11 pp., arXiv: hep-th/0002023 | DOI | MR | Zbl

[17] P. Bouwknegt, A. L. Carey, V. Mathai, M. K. Murray, D. Stevenson, Commun. Math. Phys., 228:1 (2002), 17–49, arXiv: hep-th/0106194 | DOI | MR | Zbl

[18] M. Mackaay, Cah. Topol. Géom. Différ. Catég., 44:1 (2003), 39–62, arXiv: math/0106019 | MR | Zbl

[19] U. Pennig, J. K-Theory, 14:1 (2014), 47–71, arXiv: 1108.3701 | DOI | MR | Zbl

[20] D. Johnson, J. J. Millson, “Deformation spaces associated to compact hyperbolic manifolds”, Discrete Groups in Geometry and Analysis, Progress in Mathematic, 67, ed. R. Howe, Birkhäuser, Boston, MA, 1987, 48–106 | DOI | MR | Zbl

[21] R. W. Richardson, Duke Math. J., 57:1 (1988), 1–35 | DOI | MR | Zbl

[22] A. S. Sikora, Trans. Amer. Math. Soc., 364:10 (2012), 5173–5208, arXiv: 0902.2589 | DOI | MR | Zbl

[23] M. Culler, Adv. Math., 59:1 (1986), 64–70 | DOI | MR | Zbl

[24] W. M. Goldman, J. J. Millson, Inst. Hautes Étud. Sci. Publ. Math., 67 (1988), 43–96 | DOI | MR | Zbl

[25] S. Lawton, D. Ramras, New York J. Math., 21 (2015), 383–416, arXiv: 1402.0781 | MR | Zbl

[26] W. M. Goldman, Invent. Math., 93:3 (198 8), 557–607 | DOI | MR | Zbl

[27] S. Boyer, X. Zhang, Ann. Math., 148:3 (1998), 737–801, arXiv: math/9811182 | DOI | MR | Zbl

[28] M. K. Murray, D. Stevenson, J. London Math. Soc., 62:3 (2000), 925–937, arXiv: math/9908135 | DOI | MR | Zbl

[29] A. Clifford, Ann. Math., 38:3 (1937), 533–550 | DOI | MR | Zbl

[30] N. Burbaki, Gruppy i algebry Li, gl. II, III, Mir, M., 1972 | MR

[31] R. C. Lyndon, Duke Math. J., 15:1 (1948), 271–292 | DOI | MR | Zbl

[32] G. Hochschild, J.-P. Serre, Trans. Amer. Math. Soc., 74 (1953), 110–134 | DOI | MR | Zbl

[33] E. Lupercio, B. Uribe, Commun. Math. Phys., 245:3 (2004), 449–489, arXiv: math/0105039 | DOI | MR | Zbl

[34] J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Progress in Mathematics, 107, Birkhäuser, Boston, MA, 1993 | DOI | MR | Zbl