대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권1호
  • /
  • Pages.113-122
  • /
  • 2023
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

LENS SPACES ADMITTING MINIMAL SYMPLECTIC FILLINGS WITH THE SECOND BETTI NUMBER ONE

  • Heesang, Park (Department of Mathematics Konkuk University) ;
  • Dongsoo, Shin (Department of Mathematics Chungnam National University)
  • 투고 : 2021.12.24
  • 심사 : 2022.04.22
  • 발행 : 2023.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We classify lens spaces with the Milnor fillable contact structure that admit minimal symplectic fillings whose second Betti numbers are one.

키워드

과제정보

Dongsoo Shin was supported by research fund of Chungnam National University in 2020. The authors would like to thank Korea Institute for Advanced Study for warm hospitality when they were associate members in KIAS.

참고문헌

  1. K. Behnke and J. A. Christophersen, M-resolutions and deformations of quotient surface singularities, Amer. J. Math. 116 (1994), no. 4, 881-903. https://doi.org/10.2307/2375004
  2. R. Fintushel and R. Stern, Rational blowdowns of smooth 4-manifolds, J. Differential Geom. 46 (1997), no. 2, 181-235.
  3. R. Hacking, J. Tevelev, and G. Urzua, Flipping surfaces, J. Algebraic Geom. 26 (2017), no. 2, 279-345.
  4. J. Kollar and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299-338. https://doi.org/10.1007/BF01389370
  5. P. Lisca, On symplectic fillings of lens spaces, Trans. Amer. Math. Soc. 360 (2008), no. 2, 765-799. https://doi.org/10.1090/S0002-9947-07-04228-6
  6. A. Nemethi and P. Popescu-Pampu, On the Milnor fibres of cyclic quotient singularities, Proc. Lond. Math. Soc. 101 (2010), no. 2, 554-588. https://doi.org/10.1112/plms/pdq007
  7. J. Park, Seiberg-Witten invariants of generalised rational blow-downs, Bull. Austral. Math. Soc. 56 (1997), no. 3, 363-384. https://doi.org/10.1017/S0004972700031154
  8. H. Park, J. Park, D. Shin, and G. Urzua, Milnor fibers and symplectic fillings of quotient surface singularities, Adv. Math. 329 (2018), 1156-1230. https://doi.org/10.1016/j.aim.2018.03.002
  9. M. Symington, Generalized symplectic rational blowdowns, Algebr. Geom. Topol. 1 (2001), 503-518. https://doi.org/10.2140/agt.2001.1.503
  10. G. Urzua and N. Vilches, On wormholes in the moduli space of surfaces, arXiv:2102.02177.