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

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

Published electronically:
May 18, 2000

MathSciNet review:
1676340

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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]**Atiyah, M.F.: Magnetic monopoles on hyperbolic spaces. In Proc. of Bombay Colloquium 1984 on ``Vector Bundles on Algebraic Varieties", 1987, 1-34, Oxford: Oxford University Press. MR**88i:32045****[AB]**Atiyah, M.F., and Bott, R.: The Yang-Mills equation over Riemann surfaces, Phil. Trans. R. Soc. Lond. A 308 (1982), 523-615. MR**85k:14006****[Ba]**Braam, P.J.: Magnetic Monopoles on three-manifolds, J. Differential Geometry Vol. 30 (1989), 425-464. MR**90e:53040****[DK]**Donaldson, S.K., and Kronheimer, P.B.: ``The Geometry of Four-Manifolds'', Oxford mathematical monographs, 1990, Oxford: Oxford University Press. MR**92a:57036****[G]**Gritsch, U.: Morse theory for the Yang-Mills functional via equivariant homotopy theory, 1997, preprint.**[Se]**Segal, G.B.: Equivariant K-theory, Publ. Math. Inst. Hautes Études Sci. 34 (1968), 129-151. MR**38:2769****[T]**Taubes, C.H.: Monopoles and Maps from to , the Topology of the Configuration Space, Commun. Math. Phys. 95 (1984), 345-391. MR**86i:58032****[Wa]**Wasserman, A.G.: Equivariant differential topology, Topology Vol. 8, 127-150. MR**40:3563**

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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