Volume 17, issue 1 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Other MSP Journals
Double $L$–groups and doubly slice knots

Patrick Orson

Algebraic & Geometric Topology 17 (2017) 273–329
Bibliography
1 E Bayer-Fluckiger, N W Stoltzfus, Stably hyperbolic 𝜖–Hermitian forms and doubly sliced knots, J. Reine Angew. Math. 366 (1986) 129 MR833015
2 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L2–signatures, Ann. of Math. 157 (2003) 433 MR1973052
3 D Crowley, W Lück, T Macko, Surgery theory, unpublished textbook in progress (2015)
4 R H Fox, A quick trip through knot theory, from: "Topology of 3–manifolds and related topics", Prentice Hall (1962) 120 MR0140099
5 C Kearton, Cobordism of knots and Blanchfield duality, J. London Math. Soc. 10 (1975) 406 MR0385873
6 C Kearton, Simple knots which are doubly-null-cobordant, Proc. Amer. Math. Soc. 52 (1975) 471 MR0380817
7 M A Kervaire, Les nœuds de dimensions supérieures, Bull. Soc. Math. France 93 (1965) 225 MR0189052
8 T Kim, New obstructions to doubly slicing knots, Topology 45 (2006) 543 MR2218756
9 C F Letsche, An obstruction to slicing knots using the eta invariant, Math. Proc. Cambridge Philos. Soc. 128 (2000) 301 MR1735303
10 J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229 MR0246314
11 J Levine, Knot modules, I, Trans. Amer. Math. Soc. 229 (1977) 1 MR0461518
12 J Levine, Doubly sliced knots and doubled disk knots, Michigan Math. J. 30 (1983) 249 MR718271
13 J P Levine, Metabolic and hyperbolic forms from knot theory, J. Pure Appl. Algebra 58 (1989) 251 MR1004605
14 C Livingston, J Meier, Doubly slice knots with low crossing number, New York J. Math. 21 (2015) 1007 MR3425633
15 J Meier, Distinguishing topologically and smoothly doubly slice knots, J. Topol. 8 (2015) 315 MR3356764
16 P Orson, Double L–theory, PhD thesis, University of Edinburgh (2015)
17 P Orson, Double Witt groups, preprint (2015) arXiv:1508.00383
18 M Powell, A second order algebraic knot concordance group, PhD thesis, University of Edinburgh (2011)
19 A Ranicki, The algebraic theory of surgery, I : Foundations, Proc. London Math. Soc. 40 (1980) 87 MR560997
20 A Ranicki, The algebraic theory of surgery, II : Applications to topology, Proc. London Math. Soc. 40 (1980) 193 MR566491
21 A Ranicki, Exact sequences in the algebraic theory of surgery, 26, Princeton University Press (1981) MR620795
22 A Ranicki, High-dimensional knot theory, Springer (1998) MR1713074
23 A Ranicki, Blanchfield and Seifert algebra in high-dimensional knot theory, Mosc. Math. J. 3 (2003) 1333 MR2058802
24 D Ruberman, Doubly slice knots and the Casson–Gordon invariants, Trans. Amer. Math. Soc. 279 (1983) 569 MR709569
25 D Ruberman, The Casson–Gordon invariants in high-dimensional knot theory, Trans. Amer. Math. Soc. 306 (1988) 579 MR933307
26 N W Stoltzfus, Unraveling the integral knot concordance group, 192 (1977) MR0467764
27 N W Stoltzfus, Algebraic computations of the integral concordance and double null concordance group of knots, from: "Knot theory" (editor J C Hausmann), Lecture Notes in Math. 685, Springer (1978) 274 MR521738
28 D W Sumners, Invertible knot cobordisms, Comment. Math. Helv. 46 (1971) 240 MR0290351
29 C T C Wall, Surgery on compact manifolds, 1, Academic Press (1970) MR0431216
30 C A Weibel, An introduction to homological algebra, 38, Cambridge University Press (1994) MR1269324
31 E C Zeeman, Unknotting combinatorial balls, Ann. of Math. 78 (1963) 501 MR0160218