Free genus one knots with large volume
نویسنده
چکیده
In this paper we construct families of hyperbolic knots with free genus one, whose complements have arbitrarily large volume. This implies that these knots have free genus one but arbitrarily large canonical genus.
منابع مشابه
Surgery Descriptions and Volumes of Berge Knots I: Large Volume Berge Knots
By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery descriptions for these knots on minimally twisted chain links.
متن کاملar X iv : 0 71 2 . 08 66 v 1 [ m at h . G T ] 6 D ec 2 00 7 ALEXANDER POLYNOMIALS AND HYPERBOLIC VOLUME OF ARBORESCENT LINKS
We realize a given (monic) Alexander polynomial by a (fibered) hyperbolic arborescent knot and link of any number of components, and by infinitely many such links of at least 4 components. As a consequence, a Mahler measure minimizing polynomial, if it exists, is realized as the Alexander polynomial of a fibered hyperbolic link of at least 2 components. For given polynomial, we give also an upp...
متن کاملKnots of Genus Two
We classify all knot diagrams of genus two and three, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3and 4-move conjectures, and the calculation of the maximal hyperbolic volume for weak genus two knots. We also study the values of the link polynomial...
متن کاملAdditivity of Free Genus of Knots
We show that free genus of knots is additive under connected sum.
متن کاملFree Seifert surfaces and disk decompositions
In this paper we construct families of knots which have genus one free Seifert surfaces which are not disk decomposable.
متن کامل