Geodesic
Seifert forms and concordance
Livingston, Charles1
1 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA
Geometry & topology, Tome 6 (2002) no. 1, pp. 403-408.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

If a knot K has Seifert matrix V K and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non–concordant knots having Seifert matrix V K.

DOI : 10.2140/gt.2002.6.403
Keywords: concordance, Seifert matrix, Alexander polynomial

Livingston, Charles 1

1 Department of Mathematics, Indiana University, Bloomington, Indiana 47405, USA 
@article{GT_2002_6_1_a13,
     author = {Livingston, Charles},
     title = {Seifert forms and concordance},
     journal = {Geometry & topology},
     pages = {403--408},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2002},
     doi = {10.2140/gt.2002.6.403},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.403/}
}
TY  - JOUR
AU  - Livingston, Charles
TI  - Seifert forms and concordance
JO  - Geometry & topology
PY  - 2002
SP  - 403
EP  - 408
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.403/
DO  - 10.2140/gt.2002.6.403
ID  - GT_2002_6_1_a13
ER  - 
%0 Journal Article
%A Livingston, Charles
%T Seifert forms and concordance
%J Geometry & topology
%D 2002
%P 403-408
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.403/
%R 10.2140/gt.2002.6.403
%F GT_2002_6_1_a13
Livingston, Charles. Seifert forms and concordance. Geometry & topology, Tome 6 (2002) no. 1, pp. 403-408. doi : 10.2140/gt.2002.6.403. http://geodesic.mathdoc.fr/articles/10.2140/gt.2002.6.403/

[1] A J Casson, C M Gordon, Cobordism of classical knots, from: "À la recherche de la topologie perdue", Progr. Math. 62, Birkhäuser (1986) 181

[2] T D Cochran, K E Orr, P Teichner, Knot concordance, Whitney towers and $L^2$–signatures, Ann. of Math. $(2)$ 157 (2003) 433

[3] R H Fox, Free differential calculus III: Subgroups, Ann. of Math. $(2)$ 64 (1956) 407

[4] M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357

[5] M H Freedman, F Quinn, Topology of 4–manifolds, Princeton Mathematical Series 39, Princeton University Press (1990)

[6] P M Gilmer, Slice knots in $S^{3}$, Quart. J. Math. Oxford Ser. $(2)$ 34 (1983) 305

[7] P Gilmer, C Livingston, The Casson–Gordon invariant and link concordance, Topology 31 (1992) 475

[8] B J Jiang, A simple proof that the concordance group of algebraically slice knots is infinitely generated, Proc. Amer. Math. Soc. 83 (1981) 189

[9] T Kim, Filtration of the classical knot concordance group and Casson–Gordon invariants, Math. Proc. Cambridge Philos. Soc. 137 (2004) 293

[10] S Lang, Algebra, Addison-Wesley Publishing Company Advanced Book Program (1984)

[11] S Lang, Algebraic number theory, Addison-Wesley Publishing Co., Reading, MA-London-Don Mills, Ont. (1970)

[12] J Levine, Knot cobordism groups in codimension two, Comment. Math. Helv. 44 (1969) 229

[13] J Levine, Invariants of knot cobordism, Invent. Math. 8 $(1969)$, 98–110; addendum, ibid. 8 (1969) 355

[14] R A Litherland, Cobordism of satellite knots, from: "Four-manifold theory (Durham, N.H., 1982)", Contemp. Math. 35, Amer. Math. Soc. (1984) 327

[15] T Matumoto, On the signature invariants of a non-singular complex sesquilinear form, J. Math. Soc. Japan 29 (1977) 67

[16] R Riley, Growth of order of homology of cyclic branched covers of knots, Bull. London Math. Soc. 22 (1990) 287

[17] D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976)

Cité par Sources :