Sums of lens spaces bounding rational balls
Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2141-2164
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3–spheres up to rational homology cobordisms, and to determine the concordance order of each 2–bridge knot.

DOI : 10.2140/agt.2007.7.2141
Keywords: 2–bridge knots, concordance group, lens spaces, rational homology balls, connected sums

Lisca, Paolo  1

1 Dipartimento di Matematica “L. Tonelli”, Largo Bruno Pontecorvo, 5, Università di Pisa, I-56127 Pisa, ITALY
@article{10_2140_agt_2007_7_2141,
     author = {Lisca, Paolo},
     title = {Sums of lens spaces bounding rational balls},
     journal = {Algebraic and Geometric Topology},
     pages = {2141--2164},
     year = {2007},
     volume = {7},
     number = {4},
     doi = {10.2140/agt.2007.7.2141},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.2141/}
}
TY  - JOUR
AU  - Lisca, Paolo
TI  - Sums of lens spaces bounding rational balls
JO  - Algebraic and Geometric Topology
PY  - 2007
SP  - 2141
EP  - 2164
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.2141/
DO  - 10.2140/agt.2007.7.2141
ID  - 10_2140_agt_2007_7_2141
ER  - 
%0 Journal Article
%A Lisca, Paolo
%T Sums of lens spaces bounding rational balls
%J Algebraic and Geometric Topology
%D 2007
%P 2141-2164
%V 7
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.2141/
%R 10.2140/agt.2007.7.2141
%F 10_2140_agt_2007_7_2141
Lisca, Paolo. Sums of lens spaces bounding rational balls. Algebraic and Geometric Topology, Tome 7 (2007) no. 4, pp. 2141-2164. doi: 10.2140/agt.2007.7.2141

[1] G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter Co. (1985)

[2] A J Casson, J L Harer, Some homology lens spaces which bound rational homology balls, Pacific J. Math. 96 (1981) 23

[3] S K Donaldson, The orientation of Yang–Mills moduli spaces and 4–manifold topology, J. Differential Geom. 26 (1987) 397

[4] E Grigsby, D Ruberman, S Strle, Knot concordance and Heegaard Floer homology invariants in branched covers

[5] S Jabuka, S Naik, Order in the concordance group and Heegaard Floer homology, Geom. Topol. 11 (2007) 979

[6] R Kirby, Problems in low-dimensional topology, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 35

[7] P Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007) 429

[8] C Livingston, A survey of classical knot concordance, from: "Handbook of knot theory", Elsevier BV, Amsterdam (2005) 319

[9] C Manolescu, B Owens, A concordance invariant from the Floer homology of double branched covers

[10] P Orlik, P Wagreich, Algebraic surfaces with $k^*$–action, Acta Math. 138 (1977) 43

[11] P Popescu-Pampu, The geometry of continued fractions and the topology of surface singularities, from: "Singularities in geometry and topology 2004", Adv. Stud. Pure Math. 46, Math. Soc. Japan (2007) 119

[12] O Riemenschneider, Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann. 209 (1974) 211

[13] L Siebenmann, Exercises sur les noeuds rationnels, mimeographed notes, Orsay (1975)

Cité par Sources :