Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Christopher William Davis"'
Publikováno v:
Transactions of the American Mathematical Society
We produce infinite families of knots $\{K^i\}_{i\geq 1}$ for which the set of cables $\{K^i_{p,1}\}_{i,p\geq 1}$ is linearly independent in the knot concordance group. We arrange that these examples lie arbitrarily deep in the solvable and bipolar f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a736b04e926d0120093924403d91d8ad
https://doi.org/10.1090/tran/8336
https://doi.org/10.1090/tran/8336
Publikováno v:
Indiana University Mathematics Journal. 69:2505-2547
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9d8b5d4032e85d469245e015d6abddb0
https://doi.org/10.1512/iumj.2020.69.8081
https://doi.org/10.1512/iumj.2020.69.8081
Autor:
Christopher William Davis
Publikováno v:
Canadian Mathematical Bulletin. 63:744-754
Any knot in $S^3$ may be reduced to a slice knot by crossing changes. Indeed, this slice knot can be taken to be the unknot. In this paper we study the question of when the same holds for knots in homology spheres. We show that a knot in a homology s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bfcda5f68a16c67e0e1f5035c9eeac18
https://doi.org/10.4153/s0008439519000791
https://doi.org/10.4153/s0008439519000791
In groundbreaking work from 2004, Cimasoni gave a geometric computation of the multivariable Conway potential function in terms of a generalization of a Seifert surface for a link called a C-complex. Lemma 3 of that paper provides a family of moves w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc18463586a61e6eb563ac525d55ae72
http://arxiv.org/abs/2105.10495
http://arxiv.org/abs/2105.10495
Publikováno v:
Journal of the London Mathematical Society. 98:59-84
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3118b7bdd0e4931fb5b430b073133106
https://doi.org/10.1112/jlms.12125
https://doi.org/10.1112/jlms.12125
We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.
Comment: 6 pages, 6 figures
Comment: 6 pages, 6 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::09f8c2aebcd58c552ceb579494d67026
Publikováno v:
Rocky Mountain J. Math. 50, no. 3 (2020), 839-850
In the 1980's Daryl Cooper introduced the notion of a C-complex (or clasp-complex) bounded by a link and explained how to compute signatures and polynomial invariants using a C-complex. Since then this was extended by works of Cimasoni, Florens, Mell
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b4b462b5d7e885d21751cfc1773e4ae1
Publikováno v:
Journal of Knot Theory and Its Ramifications. 29:2050064
In the 1950s Milnor defined a family of higher-order invariants generalizing the linking number. Even the first of these new invariants, the triple linking number, has received fruitful study since its inception. In the case that a link [Formula: see
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::59ba1e862d7d8870406cbc95a428ecdd
https://doi.org/10.1142/s0218216520500649
https://doi.org/10.1142/s0218216520500649
Publikováno v:
Advances in Mathematics. 274:263-284
In 1982 Louis Kauffman conjectured that if a knot in the 3-sphere is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed curve of self-linking zero which is itself a slice knot, or at least has
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7fd378d825643eb080b0f53c49f6e2d6
https://doi.org/10.1016/j.aim.2014.12.006
https://doi.org/10.1016/j.aim.2014.12.006
Autor:
Christopher William Davis
Publikováno v:
International Mathematics Research Notices. 2014:1973-2005
We give an explicit construction of linearly independent families of knots arbitrarily deep in the (n)-solvable filtration of the knot concordance group using the ρ-invariant defined in [12]. A difference between previous constructions of infinite r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bd01df48127994bb507f54e2e47ee2d9
https://doi.org/10.1093/imrn/rns277
https://doi.org/10.1093/imrn/rns277