Critical-exponent Sobolev norms and the slice theorem for the quotient space of connections

Pacific Journal of Mathematics

Volumn 200, Issue 1, 2001, Pages 71-118

  Feehan, Paul M N ^a,b  

^a RUTGERS UNIVERSITY   (United States)

^b TRINITY COLLEGE DUBLIN   (Ireland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011967280     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2001.200.71     Document Type: Article

References (26)

1. R.A. Adams, Sobolev Spaces, Academic Press, Orlando, FL, 1975, MR 56 #9247, Zbl 314.46.030.
2. M.F. Atiyah, N.J. Hitchin and I.M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Royal Soc. London, A 362 (1978), 425-461, MR 80d:53023, Zbl 389.53011.
3. T. Aubin, Nonlinear Analysis on Complex Manifolds. Monge-Ampère Equations, Springer, New York, 1982, MR 85j:58002, Zbl 512.53044.
4. S.K. Donaldson, The approximation of instantons, Geom. Funct. Anal., 3 (1993), 179-200, MR 94k:58030, Zbl 778.57010.
5. S.K. Donaldson and P.B. Kronheimer, The Geometry of Four-Manifolds, Oxford Univ. Press, Oxford, 1990, MR 92a:57036, Zbl 820.57002.
6. P.M.N. Feehan and T.G. Leness, PU(2) monopoles. I: Regularity, Uhlenbeck compactness, and transversality, J. Differential Geom., 49 (1998), 265-410, MR 2000e:57052.
7. _, PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees, J. Reine Angew. Math., to appear.
8. _, Donaldson invariants and wall-crossing formulas. I: Continuity of gluing and obstruction maps, submitted to a print journal.
9. _, PU(2) monopoles. Ill: Existence of gluing and obstruction maps, submitted to a print journal.
10. D. Freed and K.K. Uhlenbeck, Instantons and Four-Manifolds, 2nd ed., Springer, New York, 1991, MR 91i:57019.
11. H.B. Lawson, The Theory of Gauge Fields in Four Dimensions, Conf. Board Math. Sci., 58, Amer. Math. Soc., Providence, RI, 1985, MR 87d:58044, Zbl 597.53001.
12. H.B. Lawson and M.-L. Michelsohn, Spin Geometry, Princeton Univ. Press, Princeton, NJ, 1988.
13. P.K. Mitter and C.M. Viallet, On the bundle of connections and the gauge orbit manifold in Yang-Mills theory, Comm. Math. Phys., 79 (1981), 451-472, MR 83f:81056, Zbl 474.58004.
14. J. W. Morgan, Gauge theory and the topology of smooth four-manifolds, Harvard University lecture notes, 1988.
15. R.S. Palais, Foundations of Global Non-linear Analysis, Benjamin, New York, 1968, MR 40 #2130, Zbl 164.11102.
16. T.H. Parker, Gauge theories on four-dimensional Riemannian manifolds, Comm. Math. Phys., 85 (1982), 563-602, MR 84b:58036, Zbl 502.53022.
17. T.H. Parker and C.H. Taubes, On Witten's proof of the positive energy theorem, Comm. Math. Phys., 84 (1982), 223-238, MR 83m:83020, Zbl 528.58040.
18. I.M. Singer, Some remarks on the Gribov ambiguity, Comm. Math. Phys., 60 (1978), 7-12, MR 80d:53025, Zbl 379.53009.
19. E. Stein, Singular Integral Operators and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970, Zbl 207.13501.
20. C.H. Taubes, Self-dual Yang-Mills connections on non-self-dual 4-manifolds, J. Differential Geom., 17 (1982), 139-170, MR 83i:53055, Zbl 484.53026.
21. _, Path-connected Yang-Mills moduli spaces, J. Differential Geom., 19 (1984), 337-392, MR 85m:58049, Zbl 551.53040.
22. _, Self-dual connections on 4-manifolds with indefinite intersection matrix, J. Differential Geom., 19 (1984), 517-560, MR 86b:53025, Zbl 552.53011.
23. _, A framework for Morse theory for the Yang-Mills functional, Invent. Math., 94 (1988), 327-402, MR 90a:58035, Zbl 665.58006.
24. _, The stable topology of self-dual moduli spaces, J. Differential Geom., 29 (1989), 162-230, MR 90f:58023, Zbl 669.58005.
25. _, The existence of anti-self-dual conformal structures, J. Differential Geom., 36 (1992), 163-253, MR 93j:53063, Zbl 822.53006.
26. p bounds on curvature, Comm. Math. Phys., 83 (1982), 31-42, MR 83e:53035, Zbl 499.58019.