Zobrazeno 1 - 10
of 59
pro vyhledávání: '"57M27, 57N70"'
We address the primary decomposition of the knot concordance group in terms of the solvable filtration and higher-order von Neumann $\rho$-invariants by Cochran, Orr, and Teichner. We show that for a nonnegative integer n, if the connected sum of two
Externí odkaz:
http://arxiv.org/abs/1911.08084
Let {T_n} be the bipolar filtration of the smooth concordance group of topologically slice knots, which was introduced by Cochran, Harvey, and Horn. It is known that for each n not equal to 1 the quotient group T_n/T_{n+1} has infinite rank and T_1/T
Externí odkaz:
http://arxiv.org/abs/1911.08055
Autor:
Feller, Peter, Park, JungHwan
We determine the pairs of torus knots that have a genus one cobordism between them, with one notable exception. This is done by combining obstructions using $\nu^+$ from the Heegaard Floer knot complex and explicit constructions of cobordisms. As an
Externí odkaz:
http://arxiv.org/abs/1910.01672
Autor:
Rushworth, William
Publikováno v:
Algebr. Geom. Topol. 21 (2021) 3073-3106
A cobordism between links in thickened surfaces consists of a surface $ S $ and a $3$-manifold $M $, with $ S $ properly embedded in $ M \times I $. We show that there exist links in thickened surfaces such that if $(S,M) $ is a cobordism between the
Externí odkaz:
http://arxiv.org/abs/1907.09649
Autor:
Friedl, Stefan, Powell, Mark
We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L then the Alexander polynomial of L divides the Alexander polynomial of J.
Comment: 7 pages. Version 2 extends the result to Alexander polynomials of links. Versio
Comment: 7 pages. Version 2 extends the result to Alexander polynomials of links. Versio
Externí odkaz:
http://arxiv.org/abs/1907.09031
Autor:
Rushworth, William
Publikováno v:
Osaka J. Math. 58(4): 767-801 (October 2021)
We introduce the 2-colour parity. It is a theory of parity for a large class of virtual links, defined using the interaction between orientations of the link components and a certain type of colouring. The 2-colour parity is an extension of the Gauss
Externí odkaz:
http://arxiv.org/abs/1901.07406
For every integer g, we construct a 2-solvable and 2-bipolar knot whose topological 4-genus is greater than g. Note that 2-solvable knots are in particular algebraically slice and have vanishing Casson-Gordon obstructions. Similarly all known smooth
Externí odkaz:
http://arxiv.org/abs/1901.02060
Publikováno v:
Compositio Math. 156 (2020) 1825-1845
We consider the question of when a rational homology 3-sphere is rational homology cobordant to a connected sum of lens spaces. We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique
Externí odkaz:
http://arxiv.org/abs/1811.01433
Publikováno v:
Transactions of the American Mathematical Society, 374 no. 6, 4449-4479, 2021
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:
http://arxiv.org/abs/1806.06225
Autor:
Park, JungHwan, Powell, Mark
We define an obstruction for a knot to be Z[Z]-homology ribbon, and use this to provide restrictions on the integers that can occur as the triple linking numbers of derivative links of knots that are either homotopy ribbon or doubly slice. Our main a
Externí odkaz:
http://arxiv.org/abs/1802.00582