Geodesic
Cobordism distance on the projective space of the knot concordance group
Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1267-1288

Voir la notice de l'article provenant de la source Cambridge

DOI

We use the cobordism distance on the smooth knot concordance group $\mathcal {C}$ to measure how close two knots are to being linearly dependent. Our measure, $\Delta (\mathcal {K}, \mathcal {J})$, is built by minimizing the cobordism distance between all pairs of knots, $\mathcal {K}'$ and $\mathcal {J}'$, in cyclic subgroups containing $\mathcal {K}$ and $\mathcal {J}$. When made precise, this leads to the definition of the projective space of the concordance group, ${\mathbb P}(\mathcal {C})$, upon which $\Delta $ defines an integer-valued metric. We explore basic properties of ${\mathbb P}(\mathcal {C})$ by using torus knots $T_{2,2k+1}$. Twist knots are used to demonstrate that the natural simplicial complex $\overline {({\mathbb P}(\mathcal {C}), \Delta )}$ associated with the metric space ${\mathbb P}(\mathcal {C})$ is infinite-dimensional.
DOI : 10.4153/S0008414X23000408
Mots-clés : Knot concordance, 4-genus, algebraic concordance 
Livingston, Charles. Cobordism distance on the projective space of the knot concordance group. Canadian journal of mathematics, Tome 76 (2024) no. 4, pp. 1267-1288. doi: 10.4153/S0008414X23000408
@article{10_4153_S0008414X23000408,
     author = {Livingston, Charles},
     title = {Cobordism distance on the projective space of the knot concordance group},
     journal = {Canadian journal of mathematics},
     pages = {1267--1288},
     year = {2024},
     volume = {76},
     number = {4},
     doi = {10.4153/S0008414X23000408},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000408/}
}
TY  - JOUR
AU  - Livingston, Charles
TI  - Cobordism distance on the projective space of the knot concordance group
JO  - Canadian journal of mathematics
PY  - 2024
SP  - 1267
EP  - 1288
VL  - 76
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000408/
DO  - 10.4153/S0008414X23000408
ID  - 10_4153_S0008414X23000408
ER  - 
%0 Journal Article
%A Livingston, Charles
%T Cobordism distance on the projective space of the knot concordance group
%J Canadian journal of mathematics
%D 2024
%P 1267-1288
%V 76
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000408/
%R 10.4153/S0008414X23000408
%F 10_4153_S0008414X23000408

Cité par Sources :