By William Menasco, Morwen Thistlethwaite
This ebook is a survey of present issues within the mathematical concept of knots. For a mathematician, a knot is a closed loop in third-dimensional area: think knotting an extension wire after which remaining it up through putting its plug into its outlet. Knot conception is of relevant value in natural and utilized arithmetic, because it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot idea * Articles by way of prime global professionals * transparent exposition, now not over-technical * obtainable to readers with undergraduate historical past in arithmetic
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Example text
5. Braid groups and public key cryptography . . . . . . . . . . 6. The Nielsen–Thurston approach to the conjugacy problem in Bn . . . 7. Other solutions to the word problem . . . . . . . . . . . . 6. A potpourri of miscellaneous results . . . . . . . . . . . . . 1. Centralizers of braids and roots of braids . . . . . . . . . . 2. 3. The Tits conjecture . . . . . . . . . . . . . . . . . 4. Braid groups are torsion free: a new proof . . .
Abstract This article is about Artin’s braid group Bn and its role in knot theory. We set ourselves two goals: (i) to provide enough of the essential background so that our review would be accessible to graduate students, and (ii) to focus on those parts of the subject in which major progress was made, or interesting new proofs of known results were discovered, during the past 20 years.
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Abstract This article is about Artin’s braid group Bn and its role in knot theory.