A note on concordance properties of fibers in Seifert homology spheres
Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 754-767

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2017-081-9
Mots-clés : 57M27, 57N70, Seifert fibered, homology sphere, 3-manifold, concordance, cobordism, Heegaard Floer
Lidman, Tye; Tweedy, Eamonn. A note on concordance properties of fibers in Seifert homology spheres. Canadian mathematical bulletin, Tome 61 (2018) no. 4, pp. 754-767. doi: 10.4153/CMB-2017-081-9
@article{10_4153_CMB_2017_081_9,
     author = {Lidman, Tye and Tweedy, Eamonn},
     title = {A note on concordance properties of fibers in {Seifert} homology spheres},
     journal = {Canadian mathematical bulletin},
     pages = {754--767},
     year = {2018},
     volume = {61},
     number = {4},
     doi = {10.4153/CMB-2017-081-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-081-9/}
}
TY  - JOUR
AU  - Lidman, Tye
AU  - Tweedy, Eamonn
TI  - A note on concordance properties of fibers in Seifert homology spheres
JO  - Canadian mathematical bulletin
PY  - 2018
SP  - 754
EP  - 767
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-081-9/
DO  - 10.4153/CMB-2017-081-9
ID  - 10_4153_CMB_2017_081_9
ER  - 
%0 Journal Article
%A Lidman, Tye
%A Tweedy, Eamonn
%T A note on concordance properties of fibers in Seifert homology spheres
%J Canadian mathematical bulletin
%D 2018
%P 754-767
%V 61
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-081-9/
%R 10.4153/CMB-2017-081-9
%F 10_4153_CMB_2017_081_9

[CH81] [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.1981.96.23 Google Scholar

[DM17] [DM17] Dai, I. and Manolescu, C., Involutive Heegaard Floer homology and plumbed three-manifolds. 2017. arxiv:1 704.02020 Google Scholar

[EN85] [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] [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] [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/1214437136 Google Scholar

[FS90] [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/s3-61.1.109 Google Scholar

[Fur90] [Fur90] Furuta, M., Homology cobordism group of homology 3-spheres. Invent. Math. 100 (1990), no. 2,339-355. http://dx.doi.org/10.1007/BF01231190 Google Scholar

[Hei73] [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/10.2307/2039494 Google Scholar

[HM17] [HM17] Hendricks, K. and Manolescu, C., Involutive Heegaard Floer homology. Duke Math. J. 166 (2017), no. 7, 1211-1299. http://dx.doi.org/10.1215/00127094-3793141 Google Scholar

[KL99] [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)00039-1 Google Scholar

[Levl6] [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.2O16.31 Google Scholar

[LL11] [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.2011.11.625 Google Scholar

[Mil62] [Mil62] Milnor, J., A duality theorem for Reidemeister torsion. Ann. of Math. (2) 76 (1962), 137–147. http://dx.doi.org/10.2307/1970268 Google Scholar

[Neu80] [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] [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/BFb0075227 Google Scholar

[OS03a] [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.2003.7.185 Google Scholar

[OS03b] [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)00030-0 Google Scholar

[SavO2] [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.2002.205.465 Google Scholar

[Sie80] [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] [Tur86] Turaev, V. G., Reidemeister torsion in knot theory. Russian Math. Surveys 41 (1986), no. 1, 119–182. Google Scholar

[Wul6] [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/13029 Google Scholar

Cité par Sources :