Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-24T11:41:55.266Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on concordance properties of fibers in Seifert homology spheres

Published online by Cambridge University Press:  20 November 2018

Tye Lidman  and
Eamonn Tweedy
Tye Lidman
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA, e-mail : tlid@math.ncsu.edu
Eamonn Tweedy
Affiliation:
Department of Mathematics, Widener University, Chester, PA 19013, USA, e-mail : etweedy@widener.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we collect various properties of Seifert homology spheres from the viewpoint of Dehn surgery along a Seifert fiber. We expect that many of these are known to various experts, but include them in one place, which we hope will be useful in the study of concordance and homology cobordism.

Keywords

57M2757N70Seifert fiberedhomology sphere3-manifoldconcordancecobordismHeegaard Floer
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 754 - 767
Copyright
Copyright © Canadian Mathematical Society 2018

References

[CH81] Casson, A. J. and Harer, J. L., Some homology lens spaces which bound rational homology balls. Pacific J. Math. 96 (1981), no. 1, 23-36. http://dx.doi.org/10.2140/pjm.1981.96.23Google Scholar
[DM17] Dai, I. and Manolescu, C., Involutive Heegaard Floer homology and plumbed three-manifolds. 2017. arxiv:1 704.02020Google Scholar
[EN85] Eisenbud, D. and Neumann, W., Three-dimensional link theory and invariants of plane curve singularities. Annals of Mathematics Studies, Study 110, Princeton University Press, Princeton, NJ, 1985.Google Scholar
[FM66] Fox, R. H. and Milnor, J. W., Singulartities of 2-spheres in 4-space and cobordism of knots. Osaka J. Math. 3 (1966), no. 2, 257-267.Google Scholar
[Fre82] Freedman, M. H., The topology of four-dimensional manifolds. J. Differential Geom. 17 (1982), no. 3, 357-453. http://dx.doi.org/10.4310/jdg/1214437136Google Scholar
[FS90] Fintushel, R. and Stern, R. J., Instanton homology of Seifert fibred homology three spheres. Proc. London Math. Soc. (3) 61 (1990), no. 1,109-137. http://dx.doi.Org/10.1112/plms/s3-61.1.109Google Scholar
[Fur90] Furuta, M., Homology cobordism group of homology 3-spheres. Invent. Math. 100 (1990), no. 2,339-355. http://dx.doi.org/10.1007/BF01231190Google Scholar
[Hei73] Heil, W., 3-manifolds that are sums of solid tori and Seifert fiber spaces. Proc. Amer. Math. Soc. 37 (1973), 609–614. http://dx.doi.Org/10.2307/2039494Google Scholar
[HM17] Hendricks, K. and Manolescu, C., Involutive Heegaard Floer homology. Duke Math. J. 166 (2017), no. 7, 1211-1299. http://dx.doi.org/10.1215/00127094-3793141Google Scholar
[KL99] Kirk, P. and Livingston, C., Twisted Alexander invariants, Reidemeister torsion, and the Casson-Gordon invariants. Topology 38 (1999), no. 3, 635-661. http://dx.doi.org/10.1016/S0040-9383(98)00039-1Google Scholar
[Levl6] Levine, A. S., Non-surjective satellite operators and piecewise-linear concordance. Forum of Mathematics, Sigma 4 (2016), e34. http://dx.doi.Org/10.1017/fms.2O16.31Google Scholar
[LL11] Lecuona, A. G. and Lisca, P., Stein fillable Seifert fibered 3-manifolds. Algebr. Geom. Topol. 11 (2011), no. 2, 625-642. http://dx.doi.org/10.2140/agt.2011.11.625Google Scholar
[Mil62] Milnor, J., A duality theorem for Reidemeister torsion. Ann. of Math. (2) 76 (1962), 137–147. http://dx.doi.org/10.2307/1970268Google Scholar
[Neu80] Neumann, W., An invariant of plumbed homology 3-spheres. In: Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., 788, Springer, 1980, pp. 125–144.Google Scholar
[NZ85] Neumann, W. D. and Zagier, D., A note on an invariant of Fintushel and Stern. In: Geometry and Topology (College Park, Md., 1983/84), Lecture Notes in Math., 1167, Springer, Berlin, 1985, pp. 241–244. http://dx.doi.org/10.1007/BFb0075227Google Scholar
[OS03a] Ozsvâth, P. and Szabo, Z., On theFloer homology of plumbed three-manifolds. Geom. Topol. 7 (2003), 185–224. http://dx.doi.Org/10.2140/gt.2003.7.185Google Scholar
[OS03b] Ozsvâth, P. and Szabo, Z., Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary. Adv. Math. 173 (2003), no. 2,179-261. http://dx.doi.org/10.1016/S0001-8708(02)00030-0Google Scholar
[SavO2] Saveliev, N., Fukumoto-Furuta invariants of plumbed homology 3-spheres. Pacific J. Math. 205 (2002), no. 2,465-490. http://dx.doi.org/10.2140/pjm.2002.205.465Google Scholar
[Sie80] Siebenmann, L., On vanishing of the Rohlin invariant and nonfinitely amphicheiral homology 3-spheres. In: Topology Symposium, Siegen 1979 (Proc. Sympos., Univ. Siegen, Siegen, 1979), Lecture Notes in Math., 788, Springer, Berlin, 1980, pp. 172–222.Google Scholar
[Tur86] Turaev, V. G., Reidemeister torsion in knot theory. Russian Math. Surveys 41 (1986), no. 1, 119–182.Google Scholar
[Wul6] Wu, Z., A cabling formula for the v+ invariant. Proc. Amer. Math. Soc. 144 (2016), no. 9, 4089–4098. http://dx.doi.Org/10.1090/proc/13029Google Scholar