481 research outputs found
Euler characteristic and quadrilaterals of normal surfaces
Let be a compact 3-manifold with a triangulation . We give an
inequality relating the Euler characteristic of a surface normally embedded
in with the number of normal quadrilaterals in . This gives a relation
between a topological invariant of the surface and a quantity derived from its
combinatorial description. Secondly, we obtain an inequality relating the
number of normal triangles and normal quadrilaterals of , that depends on
the maximum number of tetrahedrons that share a vertex in .Comment: 7 pages, 1 figur
Face pairing graphs and 3-manifold enumeration
The face pairing graph of a 3-manifold triangulation is a 4-valent graph
denoting which tetrahedron faces are identified with which others. We present a
series of properties that must be satisfied by the face pairing graph of a
closed minimal P^2-irreducible triangulation. In addition we present
constraints upon the combinatorial structure of such a triangulation that can
be deduced from its face pairing graph. These results are then applied to the
enumeration of closed minimal P^2-irreducible 3-manifold triangulations,
leading to a significant improvement in the performance of the enumeration
algorithm. Results are offered for both orientable and non-orientable
triangulations.Comment: 30 pages, 57 figures; v2: clarified some passages and generalised the
final theorem to the non-orientable case; v3: fixed a flaw in the proof of
the conical face lemm
On iterated torus knots and transversal knots
A knot type is exchange reducible if an arbitrary closed n-braid
representative can be changed to a closed braid of minimum braid index by a
finite sequence of braid isotopies, exchange moves and +/- destabilizations. In
the manuscript [J Birman and NC Wrinkle, On transversally simple knots,
preprint (1999)] a transversal knot in the standard contact structure for S^3
is defined to be transversally simple if it is characterized up to transversal
isotopy by its topological knot type and its self-linking number. Theorem 2 of
Birman and Wrinkle [op cit] establishes that exchange reducibility implies
transversally simplicity. The main result in this note, establishes that
iterated torus knots are exchange reducible. It then follows as a Corollary
that iterated torus knots are transversally simple.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol5/paper21.abs.htm
Corrigendum to "Knot Floer homology detects fibred knots"
We correct a mistake on the citation of JSJ theory in \cite{Ni}. Some
arguments in \cite{Ni} are also slightly modified accordingly.Comment: 3 page
Makrofauna Tanah Perkebunan Kelapa Sawit (Elais Guineensis Jacq) Di Lahan Gambut Dengan Pemberian Bahan Organik Pada Tinggi Muka Air Tanah Berbeda
This researchaims to know the species amountd, total individual, calculate population density (K) and relative density (KR) soil macrofauna in oil palm plantation (Elais guineensis Jacq) in peatland by giving organic matter in water level is different.This research are conducted by observation, sampling for soil macrofauna of data is determined by purposive random sampling method, and data soil macrofauna results to analyzed statistic descriptive. The results showed that the amountd species, total individual, population density and relative density of soil macrofauna were higher in water levels of 40-50 cm. The giving organic matter in the soil water level is different in the first month, giving palm fronds and Mucunna bracteata produces the number of species, the total individual, population density, and density of the soil macrofauna relative higher than that of oil palm empty fruit bunches,while in the third month the species, the total individual, population density, and density of the soil makorfauna ralatif higher in the provision of oil palm empty fruit bunches and palm fronds.In water levels same produce the amountd species, total individual, population density, and relative density of soil macrofauna higher ground in water levels of 40-50 cm except amountd species in the third month
Makrofauna Tanah Perkebunan Kelapa Sawit (Elais Guineensis Jacq) Di Lahan Gambut Dengan Pemberian Bahan Organik Pada Tinggi Muka Air Tanah Berbeda
This researchaims to know the species amountd, total individual, calculate population density (K) and relative density (KR) soil macrofauna in oil palm plantation (Elais guineensis Jacq) in peatland by giving organic matter in water level is different.This research are conducted by observation, sampling for soil macrofauna of data is determined by purposive random sampling method, and data soil macrofauna results to analyzed statistic descriptive. The results showed that the amountd species, total individual, population density and relative density of soil macrofauna were higher in water levels of 40-50 cm. The giving organic matter in the soil water level is different in the first month, giving palm fronds and Mucunna bracteata produces the number of species, the total individual, population density, and density of the soil macrofauna relative higher than that of oil palm empty fruit bunches,while in the third month the species, the total individual, population density, and density of the soil makorfauna ralatif higher in the provision of oil palm empty fruit bunches and palm fronds.In water levels same produce the amountd species, total individual, population density, and relative density of soil macrofauna higher ground in water levels of 40-50 cm except amountd species in the third month
Continuous improvement in the context of organizational culture
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering; and, Thesis (M.S.)--Sloan School of Management, 1996.Includes bibliographical references (p. 114-116).by W. Jaco Smit.M.S
Spatial Graphs with Local Knots
It is shown that for any locally knotted edge of a 3-connected graph in
, there is a ball that contains all of the local knots of that edge and is
unique up to an isotopy setwise fixing the graph. This result is applied to the
study of topological symmetry groups of graphs embedded in .Comment: 20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been
clarified, and other minor revisions have been mad
The Computational Complexity of Knot and Link Problems
We consider the problem of deciding whether a polygonal knot in 3-dimensional
Euclidean space is unknotted, capable of being continuously deformed without
self-intersection so that it lies in a plane. We show that this problem, {\sc
unknotting problem} is in {\bf NP}. We also consider the problem, {\sc
unknotting problem} of determining whether two or more such polygons can be
split, or continuously deformed without self-intersection so that they occupy
both sides of a plane without intersecting it. We show that it also is in NP.
Finally, we show that the problem of determining the genus of a polygonal knot
(a generalization of the problem of determining whether it is unknotted) is in
{\bf PSPACE}. We also give exponential worst-case running time bounds for
deterministic algorithms to solve each of these problems. These algorithms are
based on the use of normal surfaces and decision procedures due to W. Haken,
with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur
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