On Standard Forms of 1-dominations between Knots with Same Gromov Volumes
نویسندگان
چکیده
Let k and k′ be two knots in the 3-sphere. Say k 1-dominates k′, if there is a proper degree 1 map f : E(k) → E(k′). Theorem: Suppose that any companion of k is prime. If k 1-dominates k′ with the same Gromov volume, then k′ can be obtained from k by finitely many de-satellizations. The condition of “same Gromov volume” clearly cannot be removed. We also give a new construction of 1-domination between knots with the same Gromov volume to show that the condition “any companion of k is prime” cannot be removed.
منابع مشابه
Open Gromov-Witten Invariants from the Augmentation Polynomial
A conjecture of Aganagic and Vafa relates the open Gromov-Witten theory of X = OP1(−1,−1) to the augmentation polynomial of Legendrian contact homology. We describe how to use this conjecture to compute genus zero, one boundary component open Gromov-Witten invariants for Lagrangian submanifolds LK ⊂ X obtained from the conormal bundles of knots K ⊂ S3. This computation is then performed for two...
متن کاملA comparative study of knotting decorations and knot tools Used in Ghaffarieh and Kabud domes of Maragheh city
Knotting is one of the most regular geometric decorations that spread with the spread of Islam. Among the different Islamic governments, the Ilkhani era is one of the most brilliant periods of prosperity and flourishing of art and architecture with the use of knot-making in Iran. Among the magnificent buildings of this period are Kabud Dome and Ghaffarieh Dome, located in Maragheh city, the ext...
متن کاملA Study on the Effect of Education by Using Simulation on Post partum Visual Blood Loss Estimation
Background: Post partum hemorrhage is one of the common causes in maternal morbidity and mortality and its outcome depends on accurate estimation of blood loss which needs acquiring skills. In this study, we decided to evaluate the effect of education on visual blood volume estimation by using simulation. Method: This prospective study was done in Mashhad University of Medical Sciences and 40 o...
متن کامل0 M ar 1 99 7 Gromov Invariants and Symplectic Maps
where the Z action is generated by (x, s, θ) 7→ (f(x), s + 1, θ). In this paper we compute the Gromov invariants of the manifolds Xf and of fiber sums of the Xf with other symplectic manifolds. This is done by expressing the Gromov invariants in terms of the Lefschetz zeta function of f and, in special cases, in terms of the Alexander polynomials of knots. The result is a large set of interesti...
متن کاملEvidence for a conjecture of Pandharipande
In [3], Pandharipande studied the relationship between the enumerative geometry of certain 3-folds and the Gromov-Witten invariants. In some good cases, enumerative invariants (which are manifestly integers) can be expressed as a rational combination of Gromov-Witten invariants. Pandharipande speculated that the same combination of invariants should yield integers even when they do not have any...
متن کامل