Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAll Known Principal Congruence Links
79
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This report lists the link diagrams in S^3 for all principal congruence link complements for which such a link diagram is known. Several unpublished link diagrams are included. Related to this, we also include one link diagram for an arithmetic regular tessellation link complement.
rate research
Read More
We enumerate all the principal congruence link complements in $S^3$, there by answering a question of W. Thurston. Related articles: Technical Report: All Principal Congruence Link Groups (arXiv:1902.04722), All Known Principal Congruence Links (arXiv:1902.04426).
This is a technical report accompanying the paper All Principal Congruence Link Groups (arXiv:1802.01275) classifying all principal congruence link complements in S^3 by the same authors. It provides a complete overview of all cases (d,I) that had to be considered, as well as describes the necessary computations and computer programs written for the classification result.
The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce is the $n$-quandle. Hoste and Shanahan gave a complete list of the knots and links which have finite $n$-quandles for some $n$. We introduce a generalization of $n$-quandles, denoted $N$-quandles (for a quandle with $k$ algebraic components, $N$ is a $k$-tuple of positive integers). We conjecture a classification of the links with finite $N$-quandles for some $N$, and we prove one direction of the classification.
We discuss when homogeneous quasipositive links are positive. In particular, we show that a homogeneous diagram of a quasipositive link whose number of Seifert circles is equal to the braid index is a positive diagram.
We define the stabilizing number $operatorname{sn}(K)$ of a knot $K subset S^3$ as the minimal number $n$ of $S^2 times S^2$ connected summands required for $K$ to bound a nullhomotopic locally flat disc in $D^4 # n S^2 times S^2$. This quantity is defined when the Arf invariant of $K$ is zero. We show that $operatorname{sn}(K)$ is bounded below by signatures and Casson-Gordon invariants and bounded above by the topological $4$-genus $g_4^{operatorname{top}}(K)$. We provide an infinite family of examples with $operatorname{sn}(K)<g_4^{operatorname{top}}(K)$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
