Geodesic
Knot concordance, Whitney towers and $L^2$-signatures
Tim D. Cochran1 ; Kent E. Orr2 ; Peter Teichner
1 Department of Mathematics, Rice University, Houston, TX 77005-1892
2 Department of Mathematics, Indiana University, 831 E. 3rd Street, Bloomington, IN 47405-73106
Annals of mathematics, Tome 157 (2003) no. 2, pp. 433-519.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We construct many examples of nonslice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. The bottom part of the filtration exhibits all classical concordance invariants, including the Casson-Gordon invariants. As a first step, we construct an infinite sequence of new obstructions that vanish on slice knots. These take values in the $L$-theory of skew fields associated to certain universal groups. Finally, we use the dimension theory of von Neumann algebras to define an $L^2$-signature and use this to detect the first unknown step in our obstruction theory.
DOI : 10.4007/annals.2003.157.433

Tim D. Cochran 1 ; Kent E. Orr 2 ; Peter Teichner 

1 Department of Mathematics, Rice University, Houston, TX 77005-1892
2 Department of Mathematics, Indiana University, 831 E. 3rd Street, Bloomington, IN 47405-73106 
@article{10_4007_annals_2003_157_433,
     author = {Tim D. Cochran and Kent E. Orr and Peter Teichner},
     title = {Knot concordance, {Whitney} towers and $L^2$-signatures},
     journal = {Annals of mathematics},
     pages = {433--519},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2003},
     doi = {10.4007/annals.2003.157.433},
     mrnumber = {1973052},
     zbl = {1044.57001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.433/}
}
TY  - JOUR
AU  - Tim D. Cochran
AU  - Kent E. Orr
AU  - Peter Teichner
TI  - Knot concordance, Whitney towers and $L^2$-signatures
JO  - Annals of mathematics
PY  - 2003
SP  - 433
EP  - 519
VL  - 157
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.433/
DO  - 10.4007/annals.2003.157.433
LA  - en
ID  - 10_4007_annals_2003_157_433
ER  - 
%0 Journal Article
%A Tim D. Cochran
%A Kent E. Orr
%A Peter Teichner
%T Knot concordance, Whitney towers and $L^2$-signatures
%J Annals of mathematics
%D 2003
%P 433-519
%V 157
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.433/
%R 10.4007/annals.2003.157.433
%G en
%F 10_4007_annals_2003_157_433
Tim D. Cochran; Kent E. Orr; Peter Teichner. Knot concordance, Whitney towers and $L^2$-signatures. Annals of mathematics, Tome 157 (2003) no. 2, pp. 433-519. doi : 10.4007/annals.2003.157.433. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.433/

Cité par Sources :