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The Atiyah-Jones conjecture
Author(s):
C. P.
Boyer;
J. C.
Hurtubise;
B. M.
Mann;
R. J.
Milgram
Journal:
Bull. Amer. Math. Soc.
26
(1992),
317-321.
MSC (2000):
Primary 55P35;
Secondary 14D20, 32G13, 58D27
MathSciNet review:
1130447
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Abstract:
The purpose of this note is to announce our proof of the Atiyah-Jones conjecture concerning the topology of the moduli spaces of based -instantons over . Full details and proofs appear in our paper [BHMM1].
References:
-
- [A]
- M. F. Atiyah, Instantons in two and four dimensions, Comm. Math. Phys. 93 (1984), 437-451. MR 763752 (86m:32042)
- [AJ]
- M. F. Atiyah and J. D. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), 97-118. MR 503187 (80j:58021)
- [BHMM1]
- C. P. Boyer, J. C. Hurtubise, B. M. Mann, and R. J. Milgram, The topology of instanton moduli spaces. I: The Atiyah-Jones conjecture, Ann. of Math. (2), (to appear). MR 1217348 (94h:55010)
- [BHMM2]
- -, The topology of instanton moduli spaces. II: The Toeplitz varieties, in preparation.
- [BoMa]
- C. P. Boyer and B. M. Mann, Homology operations on instantons, J. Differential Geom. 28(1988), 423-465. MR 965223 (89m:58044)
- [D]
- S. K. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys. 93 (1984), 453-461. MR 763753 (86m:32043)
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- J. Gravesen, On the topology of spaces of holomorphic maps, Acta Math. 162 (1989), 247-286. MR 989398 (90g:32023)
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- J. C. Hurtubise, Instantons and jumping lines, Comm. Math. Phys. 105 (1986), 107-122. MR 847130 (87g:14009)
- [Hu2]
- -, The classification of monopoles for the classical groups, Comm. Math. Phys. 120 (1989), 613-641. MR 987771 (90c:53182)
- [HM]
- J. C. Hurtubise and M. K. Murray, On the construction of monopoles for the classical groups, Comm. Math. Phys. 122 (1989), 35-89. MR 994495 (91d:58037)
- [MM1]
- B. M. Mann and R. J. Milgram, Some spaces of holomorphic maps to complex Grassmann manifolds, J. Differential Geom. 33 (1991), 301-324. MR 1094457 (93e:55022)
- [MM2]
- -, On the moduli space of
monopoles and holomorphic maps to flag manifolds, preprint, UNM and Stanford University, 1991. - [T1]
- C. H. Taubes, Path-connected Yang-Mills moduli spaces, J. Differential Geom. 19 (1984), 337-392. MR 755230 (85m:58049)
- [T2]
- -, The stable topology of self-dual moduli spaces, J. Differential Geom. 29 (1989), 163-230. MR 978084 (90f:58023)
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00286-0
PII:
S 0273-0979(1992)00286-0
Copyright of article:
Copyright
1992,
American Mathematical Society
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