Mathematics

Braid and knot theory in dimension four by Seiichi Kamada

By Seiichi Kamada

Braid thought and knot idea are similar through recognized effects because of Alexander and Markov. Alexander's theorem states that any knot or hyperlink could be positioned into braid shape. Markov's theorem offers beneficial and adequate stipulations to finish that braids symbolize a similar knot or hyperlink. hence, you'll be able to use braid concept to review knot conception and vice versa. during this booklet, the writer generalizes braid conception to measurement 4. He develops the speculation of floor braids and applies it to review floor hyperlinks. particularly, the generalized Alexander and Markov theorems in measurement 4 are given. This publication is the 1st to comprise an entire evidence of the generalized Markov theorem. floor hyperlinks are studied through the movie procedure, and a few very important strategies of this system are studied. For floor braids, a number of the way to describe them are brought and built: the movie strategy, the chart description, the braid monodromy, and the braid approach. those instruments are primary to realizing and computing invariants of floor braids and floor hyperlinks. integrated is a desk of knotted surfaces with a computation of Alexander polynomials. Braid concepts are prolonged to symbolize hyperlink homotopy sessions. The booklet is aimed at a large viewers, from graduate scholars to experts. it is going to make an appropriate textual content for a graduate path and a beneficial source for researchers.

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