Get An Interactive Introduction to Knot Theory PDF

By Inga Johnson, Allison K. Henrich

ISBN-10: 0486804631

ISBN-13: 9780486804637

This well-written and fascinating quantity, meant for undergraduates, introduces knot thought, a space of turning out to be curiosity in modern arithmetic. The hands-on strategy beneficial properties many routines to be accomplished by way of readers. must haves are just a uncomplicated familiarity with linear algebra and a willingness to discover the topic in a hands-on manner.
The beginning bankruptcy bargains actions that discover the realm of knots and hyperlinks — together with video games with knots — and invitations the reader to generate their very own questions in knot idea. next chapters consultant the reader to find the formal definition of a knot, households of knots and hyperlinks, and diverse knot notations. Additional themes comprise combinatorial knot invariants, knot polynomials, unknotting operations, and digital knots.

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Extra resources for An Interactive Introduction to Knot Theory

Example text

4. 3 as a guide to write an argument that given any knot projection, the precrossings can be resolved to produce a diagram of the unknot. (Hint: There are two parts to this problem. First you must devise an algorithm to create the desired unknot diagram. ) Let K be a knot. 4, we can show that, given any diagram D for K, some number of crossings can be changed in D to produce a diagram of the unknot. Note that changing a crossing in a knot diagram is like passing the corresponding knot through itself in space.

What about when Ulysses (the unknotter) plays second? Formulate and prove two propositions about these cases. 2Pretzel Links Another fascinating collection of links is the family of pretzel links. These links are both rich in structure but also easy to visualize since they are made out of simple twists. 1. Let p, q, and r be integers. A 3-strand pretzel link Pp,q,r can be constructed as follows. Take three pairs of string segments and arrange them vertically. Twist the bottom ends of the first pair p times (in the counterclockwise direction if p > 0 and in the clockwise direction if p < 0).

1: Four concentric strands. 2: Examples of replaceable regions are shown in (a). The diagram (b) shows a nonexample of a replaceable region because it contains three strands. 2 (a). By construction, a closed n-braid diagram has an innermost region with the property that any line segment drawn from the innermost region to a point that is exterior to the link will intersect the diagram at exactly n points. We count both the under- and over-strands if the segment happens to pass through a crossing.

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An Interactive Introduction to Knot Theory by Inga Johnson, Allison K. Henrich


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