Braid and Knot Theory in Dimension Four is popular PDF and ePub book, written by Seiichi Kamada in 2002, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Braid and Knot Theory in Dimension Four can be Read Online from any device for your convenience.
Braid and Knot Theory in Dimension Four Book PDF Summary
Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it tostudy surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method arestudied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduatestudents to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.
Detail Book of Braid and Knot Theory in Dimension Four PDF
- Author : Seiichi Kamada
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821829691
- Genre : Mathematics
- Total Page : 329 pages
- Language : English
- PDF File Size : 17,8 Mb
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