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Enrique Ramírez-Losada

Publications and source records attributed to Enrique Ramírez-Losada.

6 recordsLinked to original sources
arXiv2023

A bound on the number of twice-punctured tori in a knot exterior

This paper continues a program due to Motegi regarding universal bounds for the number of non-isotopic essential $n$-punctured tori in the complement of a hyperbolic knot in $S^3$. For $n=1$, Valdez-Sánchez showed that there are at most five non-isotopic Seifert tori in the exterior of a hyperbolic knot. In this paper, we address the case $n=2$. We show that there are at most six non-isotopic, nested, essential 2-holed tori in the complement of every hyperbolic knot.

math.GT↗
arXiv2021

On non almost-fibered knots

An almost-fibered knot is a knot whose complement possesses a circular thin position in which there is one and only one weakly incompressible Seifert surface and one incompressible Seifert surface. Infinite examples of almost-fibered knots are known. In this article, we show the existence of infinitely many hyperbolic genus one knots that are not almost-fibered.

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arXiv2016

Coverings of torus knots in $S^2\times S^1$ and universals

Let $t_{α,β}\subset S^2\times S^1$ be an ordinary fiber of a Seifert fibering of $S^2\times S^1$ with two exceptional fibers of order $α$. We show that any Seifert manifold with Euler number zero is a branched covering of $S^2\times S^1$ with branching $t_{α,β}$ if $α\geq3$. We compute the Seifert invariants of the Abelian covers of $S^2\times S^1$ branched along a $t_{α,β}$. We also show that $t_{2,1}$, a non-trivial torus knot in $S^2\times S^1$, is not universal.

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arXiv2014

Circular handle decompositions of free genus one knots

We determine the structure of the circular handle decompositions of the family of free genus one knots. Namely, if k is a free genus one knot, then the handle number h(k)= 0, 1 or 2, and, if k is not fibered (that is, if h(k)>0), then k is almost fibered. For this, we develop practical techniques to construct circular handle decompositions of knots with free Seifert surfaces in the 3-sphere (and compute handle numbers of many knots), and, also, we characterize the free genus one knots with more than one Seifert surface. These results are obtained through analysis of spines of surfaces on handlebodies. Also we show that there are infinite families of free genus one knots with either h(k)=1 or h(k)=2.

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arXiv2005

Crosscap number two knots in $S^3$ with (1,1) decompositions

M. Scharlemann has recently proved that any genus one tunnel number one knot is either a satellite or 2-bridge knot, as conjectured by H. Goda and M. Teragaito; all such knots admit a (1,1) decomposition. In this paper we give a classification of the family of (1,1) knots in $S^3$ with crosscap number two (i.e., bounding an essential once-punctured Klein bottle).

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