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The Calculus of Braids (Hardcover)
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The Calculus of Braids (Hardcover)
Series: London Mathematical Society Student Texts
Expected to ship within 12 - 17 working days
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Everyone knows what braids are, whether they be made of hair,
knitting wool, or electrical cables. However, it is not so evident
that we can construct a theory about them, i.e. to elaborate a
coherent and mathematically interesting corpus of results
concerning them. This book demonstrates that there is a
resoundingly positive response to this question: braids are
fascinating objects, with a variety of rich mathematical properties
and potential applications. A special emphasis is placed on the
algorithmic aspects and on what can be called the 'calculus of
braids', in particular the problem of isotopy. Prerequisites are
kept to a minimum, with most results being established from
scratch. An appendix at the end of each chapter gives a detailed
introduction to the more advanced notions required, including
monoids and group presentations. Also included is a range of
carefully selected exercises to help the reader test their
knowledge, with solutions available.
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