DOI QR코드

DOI QR Code

EXOTIC SMOOTH STRUCTURES ON (2n + 2l - 1)CP2

  • Park, Jong-Il (DEPARTMENT OF MATHEMATICAL SCIENCES SEOUL NATIONAL UNIVERSITY) ;
  • Yun, Ki-Heon (DEPARTMENT OF MATHEMATICS SUNGSHIN WOMEN'S UNIVERSITY)
  • Received : 2009.03.19
  • Published : 2010.09.30

Abstract

As an application of 'reverse engineering' technique introduced by R. Fintushel, D. Park and R. Stern [9], we present a simple way to construct an infinite family of exotic (2n+2l-1)$\mathbb{CP}^2#$(2n+4l-1)$\overline{\mathbb{CP}}^2$'s for all $n\;{\geq}\;0$, $l\;{\geq}\;1$.

Keywords

References

  1. A. Akhmedov, Small exotic 4-manifolds, Algebr. Geom. Topol. 8 (2008), no. 3, 1781-1794. https://doi.org/10.2140/agt.2008.8.1781
  2. A. Akhmedov, R. Baykur, and B. D. Park, Constructing infinitely many smooth structures on small 4-manifolds, J. Topol. 1 (2008), no. 2, 409-428. https://doi.org/10.1112/jtopol/jtn004
  3. A. Akhmedov and B. D. Park, Exotic smooth structures on small 4-manifolds, Invent. Math. 173 (2008), no. 1, 209-223. https://doi.org/10.1007/s00222-008-0118-x
  4. D. Auroux and S. K. Donaldson, and L. Katzarkov, Luttinger surgery along Lagrangian tori and non-isotopy for singular symplectic plane curves, Math. Ann. 326 (2003), no. 1, 185-203. https://doi.org/10.1007/s00208-003-0418-9
  5. S. Baldridge and P. Kirk, Constructions of small symplectic 4-manifolds using Luttinger surgery, J. Differential Geom. 82 (2009), no. 2, 317-361. https://doi.org/10.4310/jdg/1246888487
  6. A. Cannas da Silva, Lectures on Symplectic Geometry, Lecture Notes in Mathematics, 1764. Springer-Verlag, Berlin, 2001.
  7. S. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), no. 2, 279-315. https://doi.org/10.4310/jdg/1214437665
  8. S. Donaldson, Irrationality and the h-cobordism conjecture, J. Differential Geom. 26 (1987), no. 1, 141-168. https://doi.org/10.4310/jdg/1214441179
  9. R. Fintushel, B. D. Park, and R. J. Stern, Reverse engineering small 4-manifolds, Algebr. Geom. Topol. 7 (2007), 2103-2116. https://doi.org/10.2140/agt.2007.7.2103
  10. R. Fintushel and R. Stern, Knots, links, and 4-manifolds, Invent. Math. 134 (1998), no. 2, 363-400. https://doi.org/10.1007/s002220050268
  11. R. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527-595. https://doi.org/10.2307/2118554
  12. J. Morgan, T. Mrowka, and Z. Szabo, Product formulas along $T^3$ for Seiberg-Witten invariants, Math. Res. Lett. 4 (1997), no. 6, 915-929. https://doi.org/10.4310/MRL.1997.v4.n6.a11
  13. J. Park, Exotic smooth structures on 4-manifolds, Forum Math. 14 (2002), no. 6, 915-929. https://doi.org/10.1515/form.2002.041
  14. J. Park, Exotic smooth structures on 4-manifolds. II, Topology Appl. 132 (2003), no. 2, 195-202. https://doi.org/10.1016/S0166-8641(03)00033-6
  15. C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), no. 6, 809-822. https://doi.org/10.4310/MRL.1994.v1.n6.a15

Cited by

  1. GEOGRAPHY AND BOTANY OF IRREDUCIBLE NON-SPIN SYMPLECTIC 4-MANIFOLDS WITH ABELIAN FUNDAMENTAL GROUP vol.56, pp.02, 2014, https://doi.org/10.1017/S0017089513000232