Geodesic
τ–invariants for knots in rational homology spheres
Raoux, Katherine1
1Department of Mathematics, Michigan State University, East Lansing, MI, United States
Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 1601-1640
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Ozsváth and Szabó used the knot filtration on CF̂(S3) to define the τ–invariant for knots in the 3–sphere. We generalize their construction and define a collection of τ–invariants associated to a knot K in a rational homology sphere Y . We then show that some of these invariants provide lower bounds for the genus of a surface with boundary K properly embedded in a negative-definite 4–manifold with boundary Y .

DOI : 10.2140/agt.2020.20.1601
Classification : 57M27, 57R58
Keywords: Heegaard Floer, knot invariants, genus bound, rational homology spheres

Raoux, Katherine  1

1 Department of Mathematics, Michigan State University, East Lansing, MI, United States 
@article{10_2140_agt_2020_20_1601,
     author = {Raoux, Katherine},
     title = {\ensuremath{\tau}{\textendash}invariants for knots in rational homology spheres},
     journal = {Algebraic and Geometric Topology},
     pages = {1601--1640},
     year = {2020},
     volume = {20},
     number = {4},
     doi = {10.2140/agt.2020.20.1601},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.1601/}
}
TY  - JOUR
AU  - Raoux, Katherine
TI  - τ–invariants for knots in rational homology spheres
JO  - Algebraic and Geometric Topology
PY  - 2020
SP  - 1601
EP  - 1640
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.1601/
DO  - 10.2140/agt.2020.20.1601
ID  - 10_2140_agt_2020_20_1601
ER  - 
%0 Journal Article
%A Raoux, Katherine
%T τ–invariants for knots in rational homology spheres
%J Algebraic and Geometric Topology
%D 2020
%P 1601-1640
%V 20
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2020.20.1601/
%R 10.2140/agt.2020.20.1601
%F 10_2140_agt_2020_20_1601
Raoux, Katherine. τ–invariants for knots in rational homology spheres. Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 1601-1640. doi: 10.2140/agt.2020.20.1601

[1] D Calegari, C Gordon, Knots with small rational genus, Comment. Math. Helv. 88 (2013) 85 | DOI

[2] D Celoria, On concordances in 3–manifolds, J. Topol. 11 (2018) 180 | DOI

[3] J C Cha, The structure of the rational concordance group of knots, 885, Amer. Math. Soc. (2007) | DOI

[4] M Hedden, Knot Floer homology of Whitehead doubles, Geom. Topol. 11 (2007) 2277 | DOI

[5] M Hedden, S G Kim, C Livingston, Topologically slice knots of smooth concordance order two, J. Differential Geom. 102 (2016) 353 | DOI

[6] M Hedden, A S Levine, A surgery formula for knot Floer homology, preprint (2019)

[7] M Hedden, C Livingston, D Ruberman, Topologically slice knots with nontrivial Alexander polynomial, Adv. Math. 231 (2012) 913 | DOI

[8] M Hedden, O Plamenevskaya, Dehn surgery, rational open books and knot Floer homology, Algebr. Geom. Topol. 13 (2013) 1815 | DOI

[9] T E Mark, B Tosun, Naturality of Heegaard Floer invariants under positive rational contact surgery, J. Differential Geom. 110 (2018) 281 | DOI

[10] Y Ni, Link Floer homology detects the Thurston norm, Geom. Topol. 13 (2009) 2991 | DOI

[11] Y Ni, F Vafaee, Null surgery on knots in L–spaces, Trans. Amer. Math. Soc. 372 (2019) 8279 | DOI

[12] Y Ni, Z Wu, Heegaard Floer correction terms and rational genus bounds, Adv. Math. 267 (2014) 360 | DOI

[13] P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 | DOI

[14] P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 | DOI

[15] P Ozsváth, Z Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. 159 (2004) 1159 | DOI

[16] P Ozsváth, Z Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. 159 (2004) 1027 | DOI

[17] P Ozsváth, Z Szabó, Holomorphic disks, link invariants and the multi-variable Alexander polynomial, Algebr. Geom. Topol. 8 (2008) 615 | DOI

[18] P S Ozsváth, Z Szabó, Knot Floer homology and rational surgeries, Algebr. Geom. Topol. 11 (2011) 1 | DOI

[19] J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003)

[20] L Truong, A refinement of the Ozsváth–Szabó large integer surgery formula and knot concordance, preprint (2019)

[21] V Turaev, Torsion invariants of Spinc–structures on 3–manifolds, Math. Res. Lett. 4 (1997) 679 | DOI

Cité par Sources :