scholarly journals Skein algebras of the solid torus and symmetric spatial graphs

2006 ◽  
Vol 190 ◽  
pp. 1-10 ◽  
Author(s):  
Nafaa Chbili
Keyword(s):  
Solid Torus ◽  
Spatial Graphs ◽  
Skein Algebras

Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

2021 ◽  
Vol 29 (6) ◽  
pp. 863-868
Author(s):  
Danila Shubin ◽  
◽  
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Solid Torus ◽  
Lens Space ◽  
Tubular Neighborhood ◽  
Lens Spaces ◽  
Ambient Manifold ◽  
Orientable Manifold ◽  
Smale Flows ◽  
Published Result

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.

scholarly journals NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE

2016 ◽  
Vol 4 ◽  
Author(s):  
ADAM SIMON LEVINE
Keyword(s):  
Piecewise Linear ◽  
Solid Torus ◽  
Satellite Knot

We exhibit a knot $P$ in the solid torus, representing a generator of first homology, such that for any knot $K$ in the 3-sphere, the satellite knot with pattern $P$ and companion $K$ is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot in a homology 3-sphere that does not bound a piecewise-linear disk in any homology 4-ball.

4-Punctured Tori in the Exteriors of Knots

1997 ◽  
Vol 06 (05) ◽  
pp. 659-676 ◽  
Author(s):  
Mario Eudave-Muñoz
Keyword(s):  
Infinite Family ◽  
Solid Torus ◽  
Dehn Surgery ◽  
The Core

In this paper we construct an infinite family of hyperbolic knots, each having a Dehn surgery which produces a manifold containing an incompressible torus, which hits the core of the surgered solid torus in four points, but containing no incompressible torus hitting it in less than four points.

Robot navigation algorithms using learned spatial graphs

Robotica ◽  
1986 ◽  
Vol 4 (2) ◽  
pp. 93-100 ◽  
Author(s):  
S. S. Iyengar ◽  
C. C. Jorgensen ◽  
S. V. N. Rao ◽  
C. R. Weisbin
Keyword(s):  
Robot Navigation ◽  
Sensor Data ◽  
Two Dimensional ◽  
Continuous Transition ◽  
Spatial Graph ◽  
Spatial Graphs ◽  
Navigation Algorithms ◽  
Sensor Information ◽  
Navigation Planning ◽  
Available Information

SUMMARYFinding optimal paths for robot navigation in a known terrain has been studied for some time but, in many important situations, a robot would be required to navigate in completely new or partially explored terrain. We propose a method of robot navigation which requires no pre-learned model, makes maximal use of available information, records and synthesizes information from multiple journeys, and contains concepts of learning that allow for continuous transition from local to global path optimality. The model of the terrain consists of a spatial graph and a Voronoi diagram. Using acquired sensor data, polygonal boundaries containing perceived obstacles shrink to approximate the actual obstacles surfaces, free space for transit is correspondingly enlarged, and additional nodes and edges are recorded based on path intersections and stop points. Navigation planning is gradually accelerated with experience since improved global map information minimizes the need for further sensor data acquisition. Our method currently assumes obstacle locations are unchanging, navigation can be successfully conducted using two-dimensional projections, and sensor information is precise.

Arc index of spatial graphs

2018 ◽  
Vol 90 (3) ◽  
pp. 406-415
Author(s):  
Min Jung Lee ◽  
Sungjong No ◽  
Seungsang Oh
Keyword(s):  
Spatial Graphs ◽  
Arc Index
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