Volume 12, issue 2 (2012)

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Von Neumann rho invariants and torsion in the topological knot concordance group

Christopher William Davis

Algebraic & Geometric Topology 12 (2012) 753–789
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., Stanford, Calif., 1976), Part 2", Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 39 MR520521
2 J C Cha, Topological minimal genus and L2–signatures, Algebr. Geom. Topol. 8 (2008) 885 MR2443100
3 T D Cochran, Noncommutative knot theory, Algebr. Geom. Topol. 4 (2004) 347 MR2077670
4 T D Cochran, S Harvey, C Leidy, Derivatives of knots and second-order signatures, Algebr. Geom. Topol. 10 (2010) 739 MR2606799
5 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L2–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 ρ–invariants, Duke Math. J. 137 (2007) 337 MR2309149
8 J Collins, The L(2)–signature of torus knots arXiv:1001.1329
9 J F Davis, P Kirk, Lecture notes in algebraic topology, 35, American Mathematical Society (2001) MR1841974
10 S Friedl, Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants, Algebr. Geom. Topol. 4 (2004) 893 MR2100685
11 C M Gordon, Ribbon concordance of knots in the 3–sphere, Math. Ann. 257 (1981) 157 MR634459
12 S L Harvey, Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group, Geom. Topol. 12 (2008) 387 MR2390349
13 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
14 A Kawauchi, A survey of knot theory, Birkhäuser (1996) MR1417494
15 C Kearton, Blanchfield duality and simple knots, Trans. Amer. Math. Soc. 202 (1975) 141 MR0358796
16 S G Kim, Polynomial splittings of Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 59 MR2127228
17 S G Kim, T Kim, Polynomial splittings of metabelian von Neumann rho-invariants of knots, Proc. Amer. Math. Soc. 136 (2008) 4079 MR2425750
18 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
19 J P Levine, Signature invariants of homology bordism with applications to links, from: "Knots 90 (Osaka, 1990)", de Gruyter (1992) 395 MR1177436
20 P Lisca, Sums of lens spaces bounding rational balls, Algebr. Geom. Topol. 7 (2007) 2141 MR2366190
21 C Livingston, S Naik, Obstructing four-torsion in the classical knot concordance group, J. Differential Geom. 51 (1999) 1 MR1703602
22 C Livingston, S Naik, Knot concordance and torsion, Asian J. Math. 5 (2001) 161 MR1868169
23 W Lück, L2–invariants of regular coverings of compact manifolds and CW–complexes, from: "Handbook of geometric topology", North-Holland (2002) 735 MR1886681
24 W Lück, L2 invariants from the algebraic point of view, from: "Geometric and Cohomological Methods in Group Theory" (editors M R Bridson, P H Kropholler, I J Leary), London Math. Soc. Lecture Note Series 358, Cambridge Univ. Press (2009) 63
25 W Lück, T Schick, Various L2–signatures and a topological L2–signature theorem, from: "High-dimensional manifold topology", World Sci. Publ., River Edge, NJ (2003) 362 MR2048728
26 A Tamulis, Knots of ten or fewer crossings of algebraic order 2, J. Knot Theory Ramifications 11 (2002) 211 MR1895371