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

By Inga Johnson, Allison K. Henrich

This well-written and interesting quantity, meant for undergraduates, introduces knot concept, a space of growing to be curiosity in modern arithmetic. The hands-on method good points many workouts to be accomplished through readers. must haves are just a uncomplicated familiarity with linear algebra and a willingness to discover the topic in a hands-on manner.
The establishing 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 concept. next chapters advisor the reader to find the formal definition of a knot, households of knots and hyperlinks, and diverse knot notations. Additional subject matters comprise combinatorial knot invariants, knot polynomials, unknotting operations, and digital knots.

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Sample text

Investigate whether or not the family of twist knots is distinct from torus knots. Is there a twist knot that is also a torus knot? If so, give an example. If not, explain why not. 6. 3, which is known as the knot 819. 3: The knot 819 is a torus knot. 7. Investigate whether or not the knot 819 is an alternating knot. 8. Investigate whether or not the knot T2,3 is equivalent to T3,2. Can your findings be generalized? 4Closed Braids The family of links called closed braids are a generalization of torus links.

Without cutting, so that the first link is transformed identically into the second. We imagine that our strings are highly elastic so they can be scaled up or down in size, stretched and contracted. While playing and building your intuition with the activities in this chapter, you may come up with your own questions or conjectures. 8. Perhaps you will create your own new open research question about knots or perhaps you will stumble upon the same questions that the founders of the field of knot theory have puzzled over for years.

7: An oriented R2 move. 4Nonequivalence and Invariants Now that we have a well-defined notion of equivalence for links and link diagrams, we can begin to explore the idea of nonequivalence. To show that two diagrams represent equivalent knots or links, we need only find a sequence of Reidemeister moves that transforms one into the other. But how is it possible to show that two diagrams fail to be equivalent? If you think about it, you can see that failing to find a Reidemeister sequence relating two link diagrams is not proof that the two diagrams represent different links.

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