본문 바로가기
KERD
논문KCI 등재

SYMPLECTIC 4-MANIFOLDS VIA SYMPLECTIC SURGERY ON COMPLEX SURFACE SINGULARITIES

박희상|Andr´as I. Stipsicz
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회보 (Bulletin of the KMS)|제52권 제4호|pp. 1213-1223

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

symplectic surgerysurface singularity
주제분류수학

초록

We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.

Abstract

We examine a family of isolated complex surface singularities whose exceptional curves consist of two complex curves with high genera intersecting transversally. Topological data of smoothings of these singularities are determined. We use these computations to construct symplectic 4-manifolds by replacing neighborhoods of the exceptional curves with smoothings of the singularities.

참고문헌 (19)

  1. W. Barth, "Compact Complex Surfaces" (2004), Springer-Verlag
  2. A. Durfee, "The signature of smoothings of complex surface singularities", Math. Ann, 232(1), pp.85~98 (1978)
  3. R. Fintushel, "Rational blowdowns of smooth 4–manifolds", J. Differential Geom, 46(2), pp.181~235 (1997)
  4. D. Gay, "Symplectic rational blow–down along Seifert fibered 3–manifolds", Int. Math. Res. Not. IMRN, 2007(22), pp.20~ (2007)
  5. D. Gay, "Symplectic surgeries and normal surface singularities", Algebr. Geom. Topol, 9(4), pp.2203~2223 (2009)
  6. R. Gompf, "A new construction of symplectic manifolds", Ann. of Math. (2), 142(3), pp.527~595 (1995)
  7. G. Greuel, "On the topology of smoothable singularities", Proc. Sympos. Pure Math, 40 (1983), Amer. Math. Soc
  8. C. LeBrun, "Four-dimensional Einstein manifolds, and beyond, Surveys in differential geometry: essays on Einstein manifolds", Surv. Differ. Geom, 6, pp.247~285 (1999), Int. Press
  9. J. McCarthy, "Symplectic normal connect sum", Topology, 33(4), pp.729~764 (1994)
  10. G. Megyesi, "Generalisation of the Bogomolov-Miyaoka-Yau inequality to singular sur-faces", Proc. London Math. Soc, 78(2), pp.241~282 (1999)
  11. A. Melle-Hernandez, "Milnor numbers for surface singularities", Israel J. Math, 115, pp.29~50 (2000)
  12. A. N´emethi, "Five lectures on normal surface singularities, Low Dimensional Topology", Bolyai Soc. Math. Stud, 8, pp.269~351 (1999), J´anos Bolyai Math. Soc
  13. A. N´emethi, "Resolution graph of some surface singularities. I, Singularities in algebraic and analytic geometry (San Antonio, TX, 1999)", Contemp. Math, 266, pp.89~128 (2000), Amer. Math. Soc
  14. H. Park, "Smoothings of singularities and symplectic surgery", J. Sym-plectic Geom, 12(3), pp.585~597 (2014)
  15. J. Park, "Seiberg–Witten invariants of generalised rational blow–downs", Bull. Austral. Math. Soc, 56(3), pp.363~384 (1997)
  16. A. Stipsicz, "Simply connected symplectic 4-manifolds with positive signature", Turkish J. Math, 23(1), pp.145~150 (1999)
  17. M. Symington, "Symplectic rational blowdowns", J. Differential Geom, 50(3), pp.505~518 (1998)
  18. M. Symington, "Generalized symplectic rational blowdowns", Algebr. Geom. Topol, 1, pp.503~518 (2001)
  19. C. Taubes, "The Seiberg–Witten invariants and symplectic forms", Math. Res. Lett, 1(6), pp.809~822 (1994)

관련 논문AI추천

Symplectic fillings of quotient surface singularities and minimal model program박희상, 신동수, 최학호대한수학회 · 대한수학회지2021 · 제58권 제2호Rational homology balls in Milnor fibers of cyclic quotient surface singularities박희상, 신동수대한수학회 · 대한수학회보2024 · 제61권 제6호SIMPLY CONNECTED MANIFOLDS OF DIMENSION 4k WITH TWO SYMPLECTIC DEFORMATION EQUIVALENCE CLASSES김종수한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제4호Monodromy Groups on Knot Surgery 4-manifolds윤기헌경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제4호ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS김진홍대한수학회 · 대한수학회지2010 · 제47권 제4호Rational homology disk smoothings and Lefschetz fibrations최학호대한수학회 · 대한수학회지2023 · 제60권 제1호

이 간행물의 다른 논문 (28건)

ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER Fq((x−1))Zouari Sourour, Ghorbel Rimpp. 1047-1057EXISTENCE AND LARGE TIME BEHAVIOR OF SOLUTIONS TO A FOURTH-ORDER DEGENERATE PARABOLIC EQUATIONBo Liang, Meishan Wang, Ying Wangpp. 1059-1068PERMANENCE OF A TWO SPECIES DELAYED COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTINGYusen Zu, Changjin Xupp. 1069-1076EQUIVARIANT CROSSED MODULES AND COHOMOLOGY OF GROUPS WITH OPERATORSNguyen Tien Quang, Pham Thi Cucpp. 1077-1095NON-ABELIAN TENSOR ANALOGUES OF 2-AUTO ENGEL GROUPSMohammad Javad Sadeghifard, Mohammad Reza R. Moghaddampp. 1097-1105
원문 보기