Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

The Seiberg-Witten equations and 4-manifold topology

Author(s): S. K. Donaldson
Journal: Bull. Amer. Math. Soc. 33 (1996), 45-70.
MSC (1991): Primary 58-02
Retrieve article in: PDF DVI PostScript

References | Similar articles | Additional information

References:

AJ
M. F. Atiyah and L. C. Jeffrey, Topological Lagrangians and cohomology, Jour. Geometry and Physics 7 (1990), 119--136, MR 92f:58025.

A
D. Austin, Equivariant Floer Theory for binary polyhedral spaces, Preprint.

AB
D. Austin and P. Braam, Equivariant Floer cohomology, Topology (To appear).

BDGW
S. Bradlow, G. Daskalopoulos, O. Garcia-Prada, R. Wentworth, Stable augmented bundles over Riemann surfaces, Vector bundles in algebraic geometry (Ed. Hitchin, Newstead, Oxbury), Cambridge UP, 1995.

D1
S. Donaldson, Connections, cohomology and the intersection forms of four manifolds, Jour. Differential Geometry 24 (1986), 275--341, MR 88g:57033.

D2
S. Donaldson, Irrationality and the h-cobordism conjecture, Jour. Differential Geometry 26 (1987), 141-168, MR 88j:57035.

D3
S. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), 257-315, MR 92a:57035.

D4
S. Donaldson, Yang-Mills invariants of four-manifolds, Geometry of low-dimensional manifolds, Vol I (Ed. Donaldson and Thomas), Cambridge UP, 1990.

DK
S. Donaldson and P. Kronheimer, The geometry of four-manifolds, Oxford UP, 1990, MR 92a:57036.

DS
S. Donaldson and D. Sullivan, Quasiconformal four-manifolds, Acta Math. 163 (1989), 181-252, MR 91d:57012.

E
N. Elkies, A characterisation of the $\mathbf{Z}^{n}$-lattice, Math. Res. Letters (To appear).

FS
R. Fintushel and R. Stern, The blowup formula for Donaldson invariants, Preprint (1994).

FM
R. Friedman and J. Morgan, Algebraic surfaces and four-manifolds: some conjectures and speculations, Bull. Amer. Math. Soc. 18 (1988), 1-19, MR 89g:57046.

FQ
R. Friedman and Z. Qin, The smooth invariance of the Kodaira dimension of a complex surface, Math. Res. Letters 1 (1994), 369-376, CMP 95:04.

Go
R. Gompf, A new construction of symplectic manifolds, Preprint (1994).

Got
L. Gottsche, Modular forms and Donaldson invariants for $4$-manifolds with $b_{+}=1$, Preprint (1995).

Gr
M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Inventiones Math. 82 (1985), 305-347, MR 87j:53053.

GL
M. Gromov and H. Lawson, The classification of simply-connected manifolds of positive scalar curvature, Ann of Math (2) 111 (1980), 423-434, MR 81h:53036.

H
N. Hitchin, The self-duality equations on a Riemann surface, Proc. Lond. Math. Soc. 55 (1987), 59-126, MR 89a:32021.

JT
A. Jaffe and C. Taubes, Vortices and monopoles, Birkhauser, 1980, MR 82m:81051.

K
P. Kronheimer, Embedded surfaces in $4$-manifolds, Proc. Int. Congress Mathematicians, Kyoto 1990, 1990, pp. (529-539), MR 93d:57066.

KL
D. Kotschick and P.Lisca, Instanton invariants of $\mathbf{C}\mathbf{P}^{2}$ via topology, preprint.

KM1
P. Kronheimer and T. Mrowka, Gauge theory for embedded surfaces, Topology 32 (1993), 773-826, MR 94k:57048.

KM2
P. Kronheimer and T. Mrowka, Recurrence relations and asymptotics for four-manifold invariants, Bull. Amer. Math. Soc. 30 (1994), 215--221, MR 94k:57046.

KM3
P. Kronheimer and T. Mrowka, The genus of embedded surfaces in the projective plane, Math. Res. Letters 1 (1994), 797-808, CMP 95:05.

L
C. LeBrun, Einstein metrics and Mostow rigidity, Math. Res. Letters 2 (1995), 1-8, CMP 95:07.

M
M. Manetti, On some components of moduli spaces of surfaces of general type, Compositio Math. 92 (1994), 285-297, CMP 94:15.

MST
J. Morgan, Z. Szabo and C. Taubes, The generalised Thom conjecture, In preparation.

PT
V. Pidstragach and A. Tyurin, Invariants of the smooth structure of an algebraic surface arising from the Dirac operator (English translation), Russian Math. Surveys (1994).

S
N. Seiberg, Phys.Lett. B 318 (1993), 469, MR 93m:14036.

SW
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in $N=2$ supersymmetric QCD, Nucl. Phys. B 431 (1994), 581-640, CMP 95:05.

St
A. Stipsicz, Donaldson invariants of certain symplectic $4$-manifolds, Crelles Journal (To appear).

Su
D. Sullivan, Exterior $d$, the local index and smoothability, IHES preprint (1995).

T1
C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822, CMP 95:05.

T2
C. Taubes, More constraints on symplectic forms from Seiberg-Witten equations, Math. Res. Letters 2 (1995), 9-14, CMP 95:07.

T3
C. Taubes, The Seiberg-Witten and the Gromov invariants, Harvard Preprint (1995).

Th
M. Thaddeus, Stable pairs, linear systems and the Verlinde formula, Inventiones Math. 117 (1994), 317-353, MR 95e:14006.

VW
C. Vafa and E. Witten, A strong coupling test of S-duality, Nucl. Phys. B (To appear), CMP 95:04.

W1
E. Witten, Topological Quantum Field Theory, Commun. Math. Phys. 117 (1988), 353-386, MR 89m:57037.

W2
E. Witten, Supersymmetric Yang-Mills theory on a four-manifold, J. Math. Phys. 35 (1994), CMP 95:01.

W3
E. Witten, Monopoles and 4-manifolds, Math. Res. Letters 1 (1994), 769-796, CMP 95:05.


Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1991): 58-02

Retrieve articles in all Journals with MSC (1991): 58-02


Additional Information:

S. K. Donaldson
Affiliation: The Mathematical Institute, Oxford University, 24-29 St. Giles, Oxford OX1 3LB, England
Email: donaldson@vax.ox.ac.uk

DOI: 10.1090/S0273-0979-96-00625-8
PII: S 0273-0979(96)00625-8
Received by editor(s): May 15, 1995
Copyright of article: Copyright 1996, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google