The homotopy type of hyperbolic monopole orbit spaces

Author:
Ursula Gritsch

Journal:
Proc. Amer. Math. Soc. **128** (2000), 3453-3460

MSC (1991):
Primary 58B05, 55P91

Published electronically:
May 18, 2000

MathSciNet review:
1676340

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We prove that the space of equivalence classes of -invariant connections on some -principle bundles over is weakly homotopy equivalent to a component of the second loop space .

**[A]**M. F. Atiyah,*Magnetic monopoles in hyperbolic spaces*, Vector bundles on algebraic varieties (Bombay, 1984) Tata Inst. Fund. Res. Stud. Math., vol. 11, Tata Inst. Fund. Res., Bombay, 1987, pp. 1–33. MR**893593****[AB]**M. F. Atiyah and R. Bott,*The Yang-Mills equations over Riemann surfaces*, Philos. Trans. Roy. Soc. London Ser. A**308**(1983), no. 1505, 523–615. MR**702806**, 10.1098/rsta.1983.0017**[Ba]**Peter J. Braam,*Magnetic monopoles on three-manifolds*, J. Differential Geom.**30**(1989), no. 2, 425–464. MR**1010167****[DK]**S. K. Donaldson and P. B. Kronheimer,*The geometry of four-manifolds*, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1990. Oxford Science Publications. MR**1079726****[G]**Gritsch, U.: Morse theory for the Yang-Mills functional via equivariant homotopy theory, 1997, preprint.**[Se]**Graeme Segal,*Equivariant 𝐾-theory*, Inst. Hautes Études Sci. Publ. Math.**34**(1968), 129–151. MR**0234452****[T]**Clifford Henry Taubes,*Monopoles and maps from 𝑆² to 𝑆²; the topology of the configuration space*, Comm. Math. Phys.**95**(1984), no. 3, 345–391. MR**765274****[Wa]**Arthur G. Wasserman,*Equivariant differential topology*, Topology**8**(1969), 127–150. MR**0250324**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
58B05,
55P91

Retrieve articles in all journals with MSC (1991): 58B05, 55P91

Additional Information

**Ursula Gritsch**

Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB, United Kingdom

Address at time of publication:
Department of Mathematics, University of California at Berkeley, Evans Hall, Berkeley, California 94705

Email:
ursula@dpmms.cam.ac.uk, ursula@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05416-2

Keywords:
Monopoles,
gauge theory,
equivariant homotopy theory

Received by editor(s):
October 30, 1998

Received by editor(s) in revised form:
January 15, 1999

Published electronically:
May 18, 2000

Additional Notes:
This note is part of the author’s Ph.D. thesis written at Stanford University, 1997. The author thanks her advisor Ralph Cohen for constant support and encouragement and the Studienstifung des deutschen Volkes for a dissertation fellowship. Part of this paper was written while the author was supported by an EPSRC Assistantship

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 2000
American Mathematical Society