Geometry & Topology Volume 19, issue 2 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

An infinite-rank summand of topologically slice knots

Jennifer Hom

Geometry & Topology 19 (2015) 1063–1110

DOI: 10.2140/gt.2015.19.1063

Bibliography

1	A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 39 MR520521
2	A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue" (editors L Guillou, A Marin), Progr. Math. 62, Birkhäuser (1986) 181 MR900252
3	A H Clifford, Note on Hahn's theorem on ordered abelian groups, Proc. Amer. Math. Soc. 5 (1954) 860 MR0067882
4	T D Cochran, R E Gompf, Applications of Donaldson's theorems to classical knot concordance, homology $3$–spheres and property $P$, Topology 27 (1988) 495 MR976591
5	T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. 157 (2003) 433 MR1973052
6	T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
7	T D Cochran, P Teichner, Knot concordance and von Neumann $\rho$–invariants, Duke Math. J. 137 (2007) 337 MR2309149
8	S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
9	H Endo, Linear independence of topologically slice knots in the smooth cobordism group, Topology Appl. 63 (1995) 257 MR1334309
10	M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
11	R E Gompf, A I Stipsicz, $4$–manifolds and Kirby calculus, Graduate Studies in Math. 20, Amer. Math. Soc. (1999) MR1707327
12	H Hahn, Über die nicht archimedischen Grössensysteme, Sitz. der K. Akad. der Wiss., Math. Nat. Kl. 116 (1907) 601
13	S Hancock, J Hom, M Newman, On the knot Floer filtration of the concordance group, J. Knot Theory Ramifications 22 (2013) MR3190122
14	M Hausner, J G Wendel, Ordered vector spaces, Proc. Amer. Math. Soc. 3 (1952) 977 MR0052045
15	M Hedden, On knot Floer homology and cabling, II, Int. Math. Res. Not. 2009 (2009) 2248 MR2511910
16	M Hedden, S G Kim, C Livingston, Topologically slice knots of smooth concordance order two, (2012) arXiv:1212.6628v1
17	M Hedden, C Livingston, D Ruberman, Topologically slice knots with nontrivial Alexander polynomial, Adv. Math. 231 (2012) 913 MR2955197
18	J Hom, A note on cabling and $L$–space surgeries, Algebr. Geom. Topol. 11 (2011) 219 MR2764041
19	J Hom, Bordered Heegaard Floer homology and the tau-invariant of cable knots, J. Topol. 7 (2014) 287 MR3217622
20	J Hom, The knot Floer complex and the smooth concordance group, Comment. Math. Helv. 89 (2014) 537 MR3260841
21	B J Jiang, A simple proof that the concordance group of algebraically slice knots is infinitely generated, Proc. Amer. Math. Soc. 83 (1981) 189 MR620010
22	M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359 MR1740682
23	J Levine, Invariants of knot cobordism, Invent. Math. 8 (1969) 98 MR0253348
24	J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
25	R Lipshitz, P Ozsváth, D Thurston, Bordered Heegaard Floer homology: Invariance and pairing, (2011) arXiv:0810.0687v4
26	C Livingston, Computations of the Ozsváth–Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735 MR2057779
27	C Livingston, Slice knots with distinct Ozsváth–Szabó and Rasmussen invariants, Proc. Amer. Math. Soc. 136 (2008) 347 MR2350422
28	C Manolescu, B Owens, A concordance invariant from the Floer homology of double branched covers, Int. Math. Res. Not. 2007 (2007) MR2363303
29	P Ozsváth, Z Szabó, Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary, Adv. Math. 173 (2003) 179 MR1957829
30	P Ozsváth, Z Szabó, Knot Floer homology and the four-ball genus, Geom. Topol. 7 (2003) 615 MR2026543
31	P Ozsváth, Z Szabó, Holomorphic disks and knot invariants, Adv. Math. 186 (2004) 58 MR2065507
32	P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 MR2168576
33	J A Rasmussen, Floer homology and knot complements, PhD thesis, Harvard University (2003)
34	J A Rasmussen, Khovanov homology and the slice genus, Invent. Math. 182 (2010) 419 MR2729272
35	J P Tobin, Knot Floer filtration classes of topologically slice knots, J. Knot Theory Ramifications 23 (2014) 1450047, 30 MR3268983