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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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 | References | Similar articles | Additional information

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 $ SU(2)$-instantons over $ {S^4}$. 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)

[Gra]
J. Gravesen, On the topology of spaces of holomorphic maps, Acta Math. 162 (1989), 247-286. MR 989398 (90g:32023)

[Hu1]
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 $ SU(n)$ 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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