Narrow Results

In this paper we study the dynamics of one-dimensional multiply connected systems, or networks, and find under what conditions the Hamiltonian is self-adjoint. These conditions give the spectrum, and impose superselection rules in the “non-Abelian” case. We discuss the spectrum and superselection rules for some special cases.

The following sections are included:

• GLOSSARY

The following sections are included:

• A General Understanding of Topology

• Knot Theory as a Branch of Topology

• The Regular Presentations of Knots

• The Equivalence Moves

• The Knot Invariants

• Elements of Group Theory

• The Fundamental Group

• The Knot Group

• The Colorization Invariants

• The Alexander Polynomial

• The Theory of Linear Homogeneous Systems

• Calculating the Alexander Polynomial

• The “minor” Alexander Polynomials

• The Meridian-Longitude Invariants

• Proving a Knot's Chirality

• Braid Theory - Skein Invariants

• Calculating the HOMFLYPT Polynomials

• Knot Theory after the HOMFLYPT

The following sections are included:

• Basic Concepts of Computer Programming

• The Dowker Notation

• Drawing the Knot

• When is a Notation Drawable?

• The “Equal Drawability” Moves

• Multiple Notations for Equivalent Knots

• Ordering the Dowker Notations

• Calculating the Notation Invariants

• A Few Examples

• The Knot Tabulation Algorithm

• The Pseudocode

• The Flowchart

• Actual Results

Please refer to full text.

The following sections are included:

• REFERENCES

• INDEX

The following sections are included:

• ACKNOWLEDGMENTS

• PREFACE

• CONTENTS