The free genus of doubled knots
نویسندگان
چکیده
منابع مشابه
Additivity of Free Genus of Knots
We show that free genus of knots is additive under connected sum.
متن کاملFree genus one knots with large volume
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.
متن کاملThe Concordance Genus of Knots
In knot concordance three genera arise naturally, g(K), g4(K), and gc(K): these are the classical genus, the 4–ball genus, and the concordance genus, defined to be the minimum genus among all knots concordant to K. Clearly 0 ≤ g4(K) ≤ gc(K) ≤ g(K). Casson and Nakanishi gave examples to show that g4(K) need not equal gc(K). We begin by reviewing and extending their results. For knots representin...
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 کاملKNOTS OF GENUS ONE Or on the number of alternating knots of given genus
We prove that any non-hyperbolic genus one knot except the trefoil does not have a minimal canonical Seifert surface and that there are only polynomially many in the crossing number positive knots of given genus or given unknotting number.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1988
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1988-0958094-5