Geodesic
Cohomology of the Moduli Space of Rank Two, Odd Degree Vector Bundles over a Real Curve
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the moduli space of rank two, odd degree, semi-stable Real vector bundles over a real curve, calculating the singular cohomology ring in odd and zero characteristic for most examples.
Keywords: moduli space of vector bundles; gauge groups; real curves. 
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     author = {Thomas John Baird},
     title = {Cohomology of the {Moduli} {Space} of {Rank} {Two,} {Odd} {Degree} {Vector} {Bundles} over a {Real} {Curve}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a71/}
}
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Thomas John Baird. Cohomology of the Moduli Space of Rank Two, Odd Degree Vector Bundles over a Real Curve. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a71/

[1] Atiyah M. F., Bott R., “The Yang–Mills equations over Riemann surfaces”, Philos. Trans. Roy. Soc. London Ser. A, 308 (1983), 523–615 | DOI | MR | Zbl

[2] Baird T. J., “Moduli spaces of vector bundles over a real curve: $\mathbb{Z}/2$-Betti numbers”, Canad. J. Math., 66 (2014), 961–992, arXiv: 1207.4960 | DOI | MR | Zbl

[3] Baird T. J., “Classifying spaces of twisted loop groups”, Algebr. Geom. Topol., 16 (2016), 211–229, arXiv: 1312.7450 | DOI | MR | Zbl

[4] Biswas I., Huisman J., Hurtubise J., “The moduli space of stable vector bundles over a real algebraic curve”, Math. Ann., 347 (2010), 201–233, arXiv: 0901.3071 | DOI | MR | Zbl

[5] Crétois R., Real bundle automorphisms, Cauchy–Riemann operators and orientability of moduli spaces, arXiv: 1309.3110

[6] Daskalopoulos G. D., “The topology of the space of stable bundles on a compact Riemann surface”, J. Differential Geom., 36 (1992), 699–746 | MR | Zbl

[7] Gross B. H., Harris J., “Real algebraic curves”, Ann. Sci. École Norm. Sup. (4), 14 (1981), 157–182 | MR | Zbl

[8] Harder G., Narasimhan M. S., “On the cohomology groups of moduli spaces of vector bundles on curves”, Math. Ann., 212 (1975), 215–248 | DOI | MR | Zbl

[9] Kirwan F., “The cohomology rings of moduli spaces of bundles over Riemann surfaces”, J. Amer. Math. Soc., 5 (1992), 853–906 | DOI | MR | Zbl

[10] Liu C.-C. M., Schaffhauser F., “The Yang–Mills equations over Klein surfaces”, J. Topol., 6 (2013), 569–643, arXiv: 1109.5164 | DOI | MR | Zbl

[11] McCleary J., A user's guide to spectral sequences, Cambridge Studies in Advanced Mathematics, 58, 2nd ed., Cambridge University Press, Cambridge, 2001 | MR | Zbl

[12] Okonek C., Teleman A., “Abelian Yang–Mills theory on real tori and theta divisors of Klein surfaces”, Comm. Math. Phys., 323 (2013), 813–858, arXiv: 1011.1240 | DOI | MR | Zbl

[13] Schaffhauser F., “Moduli spaces of vector bundles over a Klein surface”, Geom. Dedicata, 151 (2011), 187–206, arXiv: 0912.0659 | DOI | MR | Zbl

[14] Schaffhauser F., “Real points of coarse moduli schemes of vector bundles on a real algebraic curve”, J. Symplectic Geom., 10 (2012), 503–534, arXiv: 1003.5285 | DOI | MR | Zbl