No Access

HOMOTOPY DECOMPOSITIONS OF GAUGE GROUPS OVER RIEMANN SURFACES AND APPLICATIONS TO MODULI SPACES

STEPHEN D. THERIAULT

Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK

https://doi.org/10.1142/S0129167X11007690Cited by:5 (Source: Crossref)

Abstract

For a prime p, the gauge group of a principal U(p)-bundle over a compact, orientable Riemann surface is decomposed up to homotopy as a product of spaces, each of which is commonly known. This is used to deduce explicit computations of the homotopy groups of the moduli space of stable vector bundles through a range, answering a question of Daskalopoulos and Uhlenbeck.

Keywords:

AMSC: 55P15, 55P35, 81T13

References

M. F. Atiyah and R. Bott, Philos. Trans. Roy. Soc. London Ser. A 308, 523 (1983). Crossref, Web of Science, Google Scholar
S. B. Bradlow, O. Garcia-Prada and P. B. Gothen, Topology 47, 203 (2008), DOI: 10.1016/j.top.2007.06.001. Crossref, Web of Science, Google Scholar
G. D. Daskalopoulos and K. K. Uhlenbeck, Topology 34, 203 (1995), DOI: 10.1016/0040-9383(94)E0014-B. Crossref, Web of Science, Google Scholar
G. Harder and M. S. Narasimhan, Math. Ann. 212, 215 (1975), DOI: 10.1007/BF01357141. Crossref, Web of Science, Google Scholar
L. C. Jeffrey and F. C. Kirwan, Ann. Math. 148, 109 (1998), DOI: 10.2307/120993. Crossref, Web of Science, Google Scholar
G. E. Lang, Pacific J. Math. 44, 201 (1973). Crossref, Web of Science, Google Scholar
C. A. McGibbon, Amer. J. Math. 106, 665 (1984), DOI: 10.2307/2374290. Crossref, Web of Science, Google Scholar
J.-P. Serre, Ann. Math. 58, 258 (1953), DOI: 10.2307/1969789. Crossref, Web of Science, Google Scholar
W. A. Sutherland, Proc. Roy. Soc. Edinburgh Sect. A 121, 185 (1992), DOI: 10.1017/S0308210500014220. Crossref, Web of Science, Google Scholar
S. D. Theriault, Algebr. Geom. Topol. 10, 535 (2010), DOI: 10.2140/agt.2010.10.535. Crossref, Web of Science, Google Scholar
H. Toda , Composition Methods in the Homotopy Groups of Spheres , Annals of Mathematics Studies 49 ( Princeton University Press , Princeton, NJ , 1962 ) . Google Scholar