Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Exotic smooth structures on $3\mathbf{CP}^2 \char93 n\overline{\mathbf{CP}}^2$, Part II


Author: B. Doug Park
Journal: Proc. Amer. Math. Soc. 128 (2000), 3067-3073
MSC (2000): Primary 57R55; Secondary 57R57, 53D35
DOI: https://doi.org/10.1090/S0002-9939-00-05358-2
Published electronically: March 2, 2000
MathSciNet review: 1664422
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

We construct exotic $3\mathbf{CP}^2 \char93 11\overline{\mathbf{CP}}^2$and $3\mathbf{CP}^2 \char93 13\overline{\mathbf{CP}}^2$ using the surgery techniques of R. Fintushel and R.J. Stern. We show that these 4-manifolds are irreducible by computing their Seiberg-Witten invariants.


References [Enhancements On Off] (What's this?)

  • [B] R. Barlow: A simply connected surface of general type with $p_g =0$, Invent. math. 79 (1985), 293-301. MR 87a:14033
  • [F] R. Fintushel: Lecture at the Topology and Geometry Conference, University of Århus, 1998.
  • [FS1] R. Fintushel and R.J. Stern: Immersed Spheres in 4-Manifolds and The Immersed Thom Conjecture, Turkish J. of Math. 19 (1995), 145-157. MR 96j:57036
  • [FS2] R. Fintushel and R.J. Stern: Knots, Links and 4-manifolds, to appear in Invent. math.
  • [FQ] M.H. Freedman and F. Quinn: Topology of 4-Manifolds, Princeton University Press, 1990. MR 94b:57021
  • [G] R.E. Gompf: A new construction of symplectic manifolds, Annals of Math. 142 (1995), 527-595. MR 96j:57025
  • [GS] R.E. Gompf and A.I. Stipsicz: An Introduction to 4-Manifolds and Kirby Calculus, preprint.
  • [LL] B.H. Li and T.J. Li: Minimal genus smooth embeddings in $S^2 \times S^2$ and $\mathbf{CP}^2\char93 n{\overline {\mathbf{CP}}^2}$ with $n\leq 8$, Topology 37 (1998), 575-594. MR 99b:57059
  • [MST] J.W. Morgan, Z. Szabó and C.H. Taubes: A Product Formula for the Seiberg-Witten Invariants and the Generalized Thom Conjecture, J. Diff. Geom. 44 (1996), 706-788. MR 97m:57052
  • [OS] P. Ozsváth and Z. Szabó: The symplectic Thom conjecture, preprint.
  • [P] B.D. Park: Exotic smooth structures on $3\mathbf{CP}^2\char93 n{\overline {\mathbf{CP}}^2}$, this issue.
  • [Sa] D. Salamon: Spin Geometry and Seiberg-Witten Invariants, preprint.
  • [Sz] Z. Szabó: Irreducible four-manifolds with small Euler characteristics, Topology 35 (1996), 411-426. MR 97c:57021
  • [T] C.H. Taubes: The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1 (1994), 809-822. MR 95j:57039

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 57R55, 57R57, 53D35

Retrieve articles in all journals with MSC (2000): 57R55, 57R57, 53D35


Additional Information

B. Doug Park
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: bahnpark@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05358-2
Received by editor(s): September 25, 1998
Received by editor(s) in revised form: November 2, 1998
Published electronically: March 2, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society