Bounding canonical genus bounds volume
نویسنده
چکیده
In this paper we show that there is an upper bound on the volume of a hyperbolic knot in the 3-sphere with canonical genus g. This bound can in fact be chosen to be linear in g. In other words, if Seifert's algorithm builds a surface with small genus for a hyperbolic knot, then the complement of the knot cannot have large
منابع مشابه
Entropy of Bounding Tori
Branched manifolds that describe strange attractors in R can be enclosed in, and are organized by, canonical bounding tori. Tori of genus g are labeled by a symbol sequence, or “periodic orbit”, of period g−1. We show that the number of distinct canonical bounding tori grows exponentially like N(g) ∼ eλ(g−1), with e = 3, so that the “bounding tori entropy” is log(3).
متن کاملAutomatic Bounding Estimation in Modified Nlms Algorithm
Modified Normalized Least Mean Square (MNLMS) algorithm, which is a sign form of NLMS based on set-membership (SM) theory in the class of optimal bounding ellipsoid (OBE) algorithms, requires a priori knowledge of error bounds that is unknown in most applications. In a special but popular case of measurement noise, a simple algorithm has been proposed. With some simulation examples the performa...
متن کاملBounds on the quality of the PCA bounding boxes
Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in R. The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimumvolume bounding boxes. We present examples of discrete points sets in the plane, showing that the worst case ratio of the volume of the PCA bou...
متن کاملDetecting Collisions in Graph-Driven Motion Synthesis
In this paper we consider detecting collisions between characters whose motion is specified by motion capture data. We consider rough collisions, modeling the characters as a disk in the floor plane. To provide efficient collision detection, we introduce a hierarchical bounding volume, the Motion Oriented Bounding Box tree (MOBB tree). A MOBBtree stores space-time bounds of a motion clip. In cr...
متن کاملBound Coherence for Minimum Distance Computations
Minimum distance computations on complex geometry commonly employ hierarchies of bounding volumes that are pruned through establishment of upper and lower bounds. In this paper we describe a novel time coherence scheme which utilizes coherence on these bounds, rather than coherence derived from the geometry of the bounding volumes or from the geometry of the underlying model. This method is thu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998