$\require{mediawiki-texvc}$
  • 검색어에 아래의 연산자를 사용하시면 더 정확한 검색결과를 얻을 수 있습니다.
  • 검색연산자
검색연산자 기능 검색시 예
() 우선순위가 가장 높은 연산자 예1) (나노 (기계 | machine))
공백 두 개의 검색어(식)을 모두 포함하고 있는 문서 검색 예1) (나노 기계)
예2) 나노 장영실
| 두 개의 검색어(식) 중 하나 이상 포함하고 있는 문서 검색 예1) (줄기세포 | 면역)
예2) 줄기세포 | 장영실
! NOT 이후에 있는 검색어가 포함된 문서는 제외 예1) (황금 !백금)
예2) !image
* 검색어의 *란에 0개 이상의 임의의 문자가 포함된 문서 검색 예) semi*
"" 따옴표 내의 구문과 완전히 일치하는 문서만 검색 예) "Transform and Quantization"
쳇봇 이모티콘
안녕하세요!
ScienceON 챗봇입니다.
궁금한 것은 저에게 물어봐주세요.

논문 상세정보

ON THE TOPOLOGY OF DIFFEOMORPHISMS OF SYMPLECTIC 4-MANIFOLDS

Abstract

For a closed symplectic 4-manifold X, let $Diff_0$(X) be the group of diffeomorphisms of X smoothly isotopic to the identity, and let Symp(X) be the subgroup of $Diff_0$(X) consisting of symplectic automorphisms. In this paper we show that for any finitely given collection of positive integers {$n_1$, $n_2$, $\ldots$, $n_k$} and any non-negative integer m, there exists a closed symplectic (or K$\ddot{a}$hler) 4-manifold X with $b_2^+$ (X) > m such that the homologies $H_i$ of the quotient space $Diff_0$(X)/Symp(X) over the rational coefficients are non-trivial for all odd degrees i = $2n_1$ - 1, $\ldots$, $2n_k$ - 1. The basic idea of this paper is to use the local invariants for symplectic 4-manifolds with contact boundary, which are extended from the invariants of Kronheimer for closed symplectic 4-manifolds, as well as the symplectic compactifications of Stein surfaces of Lisca and Mati$\acute{c}$.

참고문헌 (25)

  1. B. Aebischer et al., Symplectic Geometry, An introduction based on the seminar in Bern, 1992. Progress in Mathematics, 124. Birkhauser Verlag, Basel, 1994. 
  2. S. Akbulut and B. Ozbagci, On the topology of compact Stein surfaces, Int. Math. Res. Not. 2002 (2002), no. 15, 769-782. 
  3. S. Bradlow, Vortices in holomorphic line bundles over closed Kahler manifolds, Comm. Math. Phys. 135 (1990), no. 1, 1-17. 
  4. D. Eisenbud and W. Neumann, Three-dimensional Link Theory and Invariants of Plane Curve Singularities, Annals of Mathematics Studies, 110. Princeton University Press, Princeton, NJ, 1985. 
  5. Y. Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Internat. J. Math. 1 (1990), no. 1, 29-46. 
  6. Y. Eliashberg, Legendrian and transversal knots in tight contact 3-manifolds, Topological methods in modern mathematics (Stony Brook, NY, 1991), 171-193, Publish or Perish, Houston, TX, 1993. 
  7. R. Gompf, Handlebody construction of Stein surfaces, Ann. of Math. (2) 148 (1998), no. 2, 619-693. 
  8. R. Gompf and A. Stipsicz, 4-manifolds and Kirby Calculus, Graduate Studies in Mathematics, 20. American Mathematical Society, Providence, RI, 1999. 
  9. P. Kronheimer, Some non-trivial families of symplectic structures, preprint (1995); available at http://math.harvard.edu/~kronheim. 
  10. P. Kronheimer and T. Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997), no. 2, 209-255. 
  11. P. Lisca and G. Matic, Tight contact structures and Seiberg-Witten invariants, Invent. Math. 129 (1997), no. 3, 509-525. 
  12. C. McMullen and C. Taubes, 4-manifolds with inequivalent symplectic forms and 3-manifolds with inequivalent fibrations, Math. Res. Lett. 6 (1999), no. 5-6, 681-696. 
  13. J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. 
  14. T. Mrowka, P. Ozsvath, and B. Yu, Seiberg-Witten monopoles on Seifert fibered spaces, Comm. Anal. Geom. 5 (1997), no. 4, 685-791. 
  15. D. Ruberman, An obstruction to smooth isotopy in dimension 4, Math. Res. Lett. 5 (1998), no. 6, 743-758. 
  16. D. Ruberman, A polynomial invariant of diffeomorphisms of 4-manifolds, Proceedings of the Kirbyfest (Berkeley, CA, 1998), 473-488 (electronic), Geom. Topol. Monogr., 2, Geom. Topol. Publ., Coventry, 1999. 
  17. D. Ruberman, Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants, Geom. Topol. 5 (2001), 895-924. 
  18. N. Saveliev, Fukumoto-Furuta invariants of plumbed homology 3-spheres, Pacific J. Math. 205 (2002), no. 2, 465-490. 
  19. P. Seidel, Lagrangian two-spheres can be symplectically knotted, J. Differential Geom. 52 (1999), no. 1, 145-171. 
  20. I. Smith, On moduli spaces of symplectic forms, Math. Res. Lett. 7 (2000), no. 5-6, 779-788. 
  21. A. Stipsicz, On Stein fillings of the 3-torus $T^3$, preprint (2001). 
  22. C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), no. 6, 809-822. 
  23. C. Taubes, More constraints on symplectic forms from Seiberg-Witten invariants, Math. Res. Lett. 2 (1995), no. 1, 9-13. 
  24. C. Taubes, SW ${\Rightarrow}$ Gr: from the Seiberg-Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996), no. 3, 845-918. 
  25. S. Vidussi, Homotopy K3's with several symplectic structures, Geom. Topol. 5 (2001), 267-285. 

이 논문을 인용한 문헌 (0)

  1. 이 논문을 인용한 문헌 없음

원문보기

원문 PDF 다운로드

  • ScienceON :
  • KCI :

원문 URL 링크

원문 PDF 파일 및 링크정보가 존재하지 않을 경우 KISTI DDS 시스템에서 제공하는 원문복사서비스를 사용할 수 있습니다. (원문복사서비스 안내 바로 가기)

상세조회 0건 원문조회 0건

DOI 인용 스타일