Volume 7 (2004)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
 
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN 1464-8997 (online)
ISSN 1464-8989 (print)
 
MSP Books and Monographs
Other MSP Publications

Whitney towers and the Kontsevich integral

Rob Schneiderman and Peter Teichner

Geometry & Topology Monographs 7 (2004) 101–134

DOI: 10.2140/gtm.2004.7.101

Bibliography
1 D Bar-Natan, Vassiliev homotopy string link invariants, J. Knot Theory Ramifications 4 (1995) 13–32 MR1321289
2 A J Casson, Three lectures on new-infinite constructions in 4–dimensional manifolds, from: "À la recherche de la topologie perdue", Progr. Math. 62, Birkhäuser (1986) 201–244 MR900253 With an appendix by L. Siebenmann
3 A J Casson, Link cobordism and Milnor's invariant, Bull. London Math. Soc. 7 (1975) 39–40 MR0362286
4 T D Cochran, Derivatives of links: Milnor's concordance invariants and Massey's products, Mem. Amer. Math. Soc. 84 (1990) MR1042041
5 T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and L²–signatures, Ann. of Math. (2) 157 (2003) 433–519 MR1973052
6 T D Cochran, P Teichner, Knot concordance and von Neumann ρ–invariants, Duke Math. J. 137 (2007) 337–379 MR2309149
7 J Conant, P Teichner, Grope cobordism of classical knots, Topology 43 (2004) 119–156 MR2030589
8 J Conant, P Teichner, Grope cobordism and Feynman diagrams, Math. Ann. 328 (2004) 135–171 MR2030373
9 J Conant, R Schneiderman, P Teichner, A geometric IHX relation in 3 and 4 dimensions, in preparation
10 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357–453 MR679066
11 M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990) MR1201584
12 C H Giffen, Link concordance implies link homotopy, Math. Scand. 45 (1979) 243–254 MR580602
13 D L Goldsmith, Concordance implies homotopy for classical links in M3, Comment. Math. Helv. 54 (1979) 347–355 MR543335
14 S Garoufalidis, A Kricker, A rational noncommutative invariant of boundary links, Geom. Topol. 8 (2004) 115–204 MR2033481
15 S Garoufalidis, J Levine, Homology surgery and invariants of 3–manifolds, Geom. Topol. 5 (2001) 551–578 MR1833753
16 K Habiro, Claspers and finite type invariants of links, Geom. Topol. 4 (2000) 1–83 MR1735632
17 N Habegger, G Masbaum, The Kontsevich integral and Milnor's invariants, Topology 39 (2000) 1253–1289 MR1783857
18 M A Kervaire, J W Milnor, On 2–spheres in 4–manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961) 1651–1657 MR0133134
19 W Magnus, A Karrass, D Solitar, Combinatorial group theory, Dover Publications (1976) MR0422434 Presentations of groups in terms of generators and relations
20 K Kobayashi, On a homotopy version of 4–dimensional Whitney's lemma, Math. Sem. Notes Kobe Univ. 5 (1977) 109–116 MR0458431
21 S Kojima, Milnor's \bar µ –invariants, Massey products and Whitney's trick in 4 dimensions, Topology Appl. 16 (1983) 43–60 MR702619
22 V S Krushkal, Exponential separation in 4–manifolds, Geom. Topol. 4 (2000) 397–405 MR1796497
23 V S Krushkal, P Teichner, Alexander duality, gropes and link homotopy, Geom. Topol. 1 (1997) 51–69 MR1475554
24 J Milnor, Link groups, Ann. of Math. (2) 59 (1954) 177–195 MR0071020
25 J Milnor, Isotopy of links. Algebraic geometry and topology, from: "A symposium in honor of S. Lefschetz", Princeton University Press (1957) 280–306 MR0092150
26 Y Matsumoto, Secondary intersectional properties of 4–manifolds and Whitney's trick, 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) 99–107 MR520526
27 G Masbaum, A Vaintrob, Milnor numbers, spanning trees, and the Alexander–Conway polynomial, Adv. Math. 180 (2003) 765–797 MR2020557
28 R Schneiderman, Whitney towers and gropes in 4–manifolds, Trans. Amer. Math. Soc. 358 (2006) 4251–4278 MR2231378
29 R Schneiderman, Simple Whitney towers, half-gropes and the Arf invariant of a knot arXiv:math.GT/0310304
30 R Schneiderman, P Teichner, Higher order intersection numbers of 2–spheres in 4–manifolds, Algebr. Geom. Topol. 1 (2001) 1–29 MR1790501
31 R Schneiderman, P Teichner, Pulling apart 2–spheres in 4–manifolds, in preparation
32 R Schneiderman, P Teichner, Grope concordance of classical links, in preparation
33 P Teichner, Knots, von Neumann signatures, and grope cobordism, from: "Proceedings of the International Congress of Mathematicians, Vol II (Beijing, 2002)", Higher Ed. Press (2002) 437–446 MR1957054
34 C T C Wall, Surgery on compact manifolds, Mathematical Surveys and Monographs 69, American Mathematical Society (1999) MR1687388 Edited and with a foreword by A. A. Ranicki
35 H Whitney, The self-intersections of a smooth n–manifold in 2n–space, Ann. of Math. (2) 45 (1944) 220–246 MR0010274
36 M Yamasaki, Whitney's trick for three 2–dimensional homology classes of 4–manifolds, Proc. Amer. Math. Soc. 75 (1979) 365–371 MR532167