The bounding genera and $w$-invariants
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- by Yoshihiro Fukumoto PDF
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Abstract:
In this paper, we give an estimate from below of the bounding genera for homology $3$-spheres defined by Y. Matsumoto in terms of $w$-invariants. In particular, combining with Matsumoto’s estimates we determine the values of the bounding genera for several infinite families of Brieskorn homology $3$-spheres.References
- Selman Akbulut and Robion Kirby, Mazur manifolds, Michigan Math. J. 26 (1979), no. 3, 259–284. MR 544597
- Andrew J. Casson and John L. Harer, Some homology lens spaces which bound rational homology balls, Pacific J. Math. 96 (1981), no. 1, 23–36. MR 634760, DOI 10.2140/pjm.1981.96.23
- Ronald Fintushel and Ronald J. Stern, Pseudofree orbifolds, Ann. of Math. (2) 122 (1985), no. 2, 335–364. MR 808222, DOI 10.2307/1971306
- Shinji Fukuhara, On the invariant for a certain type of involutions of homology $3$-spheres and its application, J. Math. Soc. Japan 30 (1978), no. 4, 653–665. MR 513075, DOI 10.2969/jmsj/03040653
- Y. Fukumoto, On an invariant of plumbed homology 3-spheres, J. Math. Kyoto Univ. 40 (2000), no. 2, 379–388. MR 1787877, DOI 10.1215/kjm/1250517719
- Y. Fukumoto, Plumbed homology $3$-spheres bounding acyclic $4$-manifolds, J. Math. Kyoto Univ. 40 (2000), no. 4, 729–749. MR 1802843, DOI 10.1215/kjm/1250517663
- Y. Fukumoto and M. Furuta, Homology 3-spheres bounding acyclic 4-manifolds, Math. Res. Lett. 7 (2000), no. 5-6, 757–766. MR 1809299, DOI 10.4310/MRL.2000.v7.n6.a8
- Yoshihiro Fukumoto, Mikio Furuta, and Masaaki Ue, $W$-invariants and Neumann-Siebenmann invariants for Seifert homology $3$-spheres, Topology Appl. 116 (2001), no. 3, 333–369. MR 1857670, DOI 10.1016/S0166-8641(00)00103-6
- M. Furuta, Monopole equation and the $\frac {11}8$-conjecture, Math. Res. Lett. 8 (2001), no. 3, 279–291. MR 1839478, DOI 10.4310/MRL.2001.v8.n3.a5
- Tetsuro Kawasaki, The index of elliptic operators over $V$-manifolds, Nagoya Math. J. 84 (1981), 135–157. MR 641150, DOI 10.1017/S0027763000019589
- Yukio Matsumoto, On the bounding genus of homology $3$-spheres, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 (1982), no. 2, 287–318. MR 672065
- Walter D. Neumann, An invariant of plumbed homology spheres, Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., vol. 788, Springer, Berlin, 1980, pp. 125–144. MR 585657
- Walter D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268 (1981), no. 2, 299–344. MR 632532, DOI 10.1090/S0002-9947-1981-0632532-8
- Walter D. Neumann and Don Zagier, A note on an invariant of Fintushel and Stern, Geometry and topology (College Park, Md., 1983/84) Lecture Notes in Math., vol. 1167, Springer, Berlin, 1985, pp. 241–244. MR 827273, DOI 10.1007/BFb0075227
- Ichirô Satake, The Gauss-Bonnet theorem for $V$-manifolds, J. Math. Soc. Japan 9 (1957), 464–492. MR 95520, DOI 10.2969/jmsj/00940464
- Nikolai Saveliev, Fukumoto-Furuta invariants of plumbed homology 3-spheres, Pacific J. Math. 205 (2002), no. 2, 465–490. MR 1922741, DOI 10.2140/pjm.2002.205.465
- L. Siebenmann, On vanishing of the Rohlin invariant and nonfinitely amphicheiral homology $3$-spheres, Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., vol. 788, Springer, Berlin, 1980, pp. 172–222. MR 585660
Additional Information
- Yoshihiro Fukumoto
- Affiliation: Department of Environmental and Information Studies, Tottori University ofEnvironmental Studies, 1-1-1 Wakabadai-Kita, Tottori 689-1111, Japan
- Email: fukumoto@kankyo-u.ac.jp
- Received by editor(s): September 26, 2007
- Received by editor(s) in revised form: May 11, 2008
- Published electronically: November 3, 2008
- Additional Notes: Research supported by MEXT Grant-in-Aid for Scientific Research (18740039)
- Communicated by: Daniel Ruberman
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1509-1517
- MSC (2000): Primary 57R57, 55N22; Secondary 58J20, 57R80
- DOI: https://doi.org/10.1090/S0002-9939-08-09744-X
- MathSciNet review: 2465677