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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

The bounding genera and $ w$-invariants

Author(s): Yoshihiro Fukumoto
Journal: Proc. Amer. Math. Soc. 137 (2009), 1509-1517.
MSC (2000): Primary 57R57, 55N22; Secondary 58J20, 57R80
Posted: November 3, 2008
MathSciNet review: 2465677
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Abstract | References | Similar articles | Additional information

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:

1.
S. Akbulut and R. Kirby, Mazur manifolds, Michigan Math. J. 26 (1979), 259-284. MR 544597 (80h:57004)

2.
A. Casson and J. Harer, Some homology lens spaces which bound rational homology balls, Pacific J. Math. 96 (1981), 23-36. MR 634760 (83h:57013)

3.
R. Fintushel and R. Stern, Pseudofree orbifolds, Ann. of Math. (2) (1985), 335-364. MR 808222 (87a:57027)

4.
S. Fukuhara, On the invariant for a certain type of involutions of homology $ 3$-spheres and its application, J. Math. Soc. Japan 30 (1978), 653-665. MR 513075 (80g:57046)

5.
Y. Fukumoto, On an invariant of plumbed homology $ 3$-spheres, J. Math. Kyoto Univ. 40-2 (2000), 379-388. MR 1787877 (2001m:57032)

6.
Y. Fukumoto, Plumbed homology $ 3$-spheres bounding acyclic $ 4$-manifolds, J. Math. Kyoto Univ. 40-4 (2000), 729-749. MR 1802843 (2002g:57065)

7.
Y. Fukumoto and M. Furuta, Homology $ 3$-spheres bounding acyclic $ 4$-manifolds, Math. Res. Lett. 7 (2000), 757-766. MR 1809299 (2001m:57063)

8.
Y. Fukumoto, M. Furuta and M. Ue, $ W$-invariants and Neumann-Siebenmann invariants for Seifert homology $ 3$-spheres, Topology and its Appl. 116 (2001), 333-369. MR 1857670 (2002j:57062)

9.
M. Furuta, Monopole equation and the $ 11/8$ conjecture, Math. Res. Lett. 8 (2001), 279-291. MR 1839478 (2003e:57042)

10.
T. Kawasaki, The index of elliptic operators over V-manifolds, Nagoya Math. J. 84 (1981), 135-137. MR 641150 (83i:58095)

11.
Y. Matsumoto, On the bounding genus of homology $ 3$-spheres, J. Fac. Sci. Univ. Tokyo Sect. IA. Math. 29 (1982), 287-318. MR 672065 (84g:57010)

12.
W. Neumann, An invariant of plumbed homology $ 3$-spheres, Lecture Notes in Math. 788, Springer-Verlag (1980), 125-144. MR 585657 (82j:57033)

13.
W. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc. 268, No. 2 (1981), 299-343. MR 632532 (84a:32015)

14.
W. Neumann and D. Zagier, A note on an invariant of Fintushel and Stern, Lecture Notes in Math. 1167, Springer, Berlin-Heidelberg (1985), 241-244. MR 827273 (87e:57020)

15.
I. Satake, The Gauss-Bonnet theorem for $ V$-manifolds, J. Math. Soc. Japan 9 (1957), 464-492. MR 0095520 (20:2022)

16.
N. Saveliev, Fukumoto-Furuta invariants of plumbed homology $ 3$-spheres, Pacific J. Math. 205 (2002), 465-490. MR 1922741 (2003k:57038)

17.
L. Siebenmann, On vanishing of the Rohlin invariant and nonfinitely amphicheiral homology $ 3$-spheres, Lecture Notes in Math. 788, Springer-Verlag (1980), 172-222. MR 585660 (81k:57011)

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Additional Information:

Yoshihiro Fukumoto
Affiliation: Department of Environmental and Information Studies, Tottori University of Environmental Studies, 1-1-1 Wakabadai-Kita, Tottori 689-1111, Japan
Email: fukumoto@kankyo-u.ac.jp

DOI: 10.1090/S0002-9939-08-09744-X
PII: S 0002-9939(08)09744-X
Received by editor(s): September 26, 2007,
Received by editor(s) in revised form: May 11, 2008
Posted: November 3, 2008
Additional Notes: Research supported by MEXT Grant-in-Aid for Scientific Research (18740039)
Communicated by: Daniel Ruberman
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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