Algebraic & Geometric Topology Volume 10, issue 2 (2010)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Derivatives of knots and second-order signatures

Tim D Cochran, Shelly Harvey and Constance Leidy

Algebraic & Geometric Topology 10 (2010) 739–787

DOI: 10.2140/agt.2010.10.739

Bibliography

1	A J Casson, C M Gordon, On slice knots in dimension three, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., 1976), Part 2" (editor R J Milgram), Proc. Sympos. Pure Math. XXXII, 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	J Cheeger, M Gromov, Bounds on the von Neumann dimension of $L^2$–cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
4	D Cimasoni, V Florens, Generalized Seifert surfaces and signatures of colored links, Trans. Amer. Math. Soc. 360 (2008) 1223 MR2357695
5	T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
6	T D Cochran, S Friedl, P Teichner, New constructions of slice links, Comment. Math. Helv. 84 (2009) 617 MR2507256
7	T D Cochran, S Harvey, Homology and derived $p$–series of groups, J. Lond. Math. Soc. $(2)$ 78 (2008) 677 MR2456898
8	T D Cochran, S Harvey, C Leidy, Knot concordance and Blanchfield duality arXiv:0705.3987
9	T D Cochran, S Harvey, C Leidy, Knot concordance and Blanchfield duality, Oberwolfach Reports 3 (2006)
10	T D Cochran, S Harvey, C Leidy, Link concordance and generalized doubling operators, Algebr. Geom. Topol. 8 (2008) 1593 MR2443256
11	T D Cochran, S Harvey, C Leidy, Knot concordance and higher-order Blanchfield duality, Geom. Topol. 13 (2009) 1419 MR2496049
12	T D Cochran, K E Orr, Homology boundary links and Blanchfield forms: concordance classification and new tangle-theoretic constructions, Topology 33 (1994) 397 MR1286923
13	T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433 MR1973052
14	T D Cochran, K E Orr, P Teichner, Structure in the classical knot concordance group, Comment. Math. Helv. 79 (2004) 105 MR2031301
15	T D Cochran, P Teichner, Knot concordance and von Neumann $\rho$–invariants, Duke Math. J. 137 (2007) 337 MR2309149
16	S Friedl, Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants, Algebr. Geom. Topol. 4 (2004) 893 MR2100685
17	P Gilmer, Slice knots in $S^{3}$, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 305 MR711523
18	P Gilmer, Classical knot and link concordance, Comment. Math. Helv. 68 (1993) 1 MR1201199
19	S Harvey, Higher-order polynomial invariants of $3$–manifolds giving lower bounds for the Thurston norm, Topology 44 (2005) 895 MR2153977
20	J A Hillman, Alexander ideals of links, Lecture Notes in Math. 895, Springer (1981) MR653808
21	P D Horn, Higher-order genera of knots arXiv:0807.0434
22	A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996) MR1417494
23	C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. $(2)$ 10 (1975) 406 MR0385873
24	T Kim, An infinite family of non-concordant knots having the same Seifert form, Comment. Math. Helv. 80 (2005) 147 MR2130571
25	C Lamm, Symmetric unions and ribbon knots, Osaka J. Math. 37 (2000) 537 MR1789436
26	C Leidy, Higher-order linking forms for $3$–manifolds, preprint
27	C F Letsche, An obstruction to slicing knots using the eta invariant, Math. Proc. Cambridge Philos. Soc. 128 (2000) 301 MR1735303
28	J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
29	W Lück, T Schick, Various $L^2$–signatures and a topological $L^2$–signature theorem, from: "High-dimensional manifold topology" (editors F T Farrell, W Lück), World Sci. Publ. (2003) 362 MR2048728
30	L Smolinsky, Invariants of link cobordism, from: "Proceedings of the 1987 Georgia Topology Conference (Athens, GA, 1987)" (editors N Habegger, C McCrory) (1989) 161 MR1007988
31	R Strebel, Homological methods applied to the derived series of groups, Comment. Math. Helv. 49 (1974) 302 MR0354896