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Books > Science & Mathematics > Mathematics > Algebra
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Operads in Algebra, Topology and Physics (Paperback)
Loot Price: R3,196
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Operads in Algebra, Topology and Physics (Paperback)
Series: Mathematical Surveys and Monographs
Expected to ship within 12 - 19 working days
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'Operads are powerful tools, and this is the book in which to read
about them' - ""Bulletin of the London Mathematical Society"".
Operads are mathematical devices that describe algebraic structures
of many varieties and in various categories. Operads are
particularly important in categories with a good notion of
'homotopy', where they play a key role in organizing hierarchies of
higher homotopies. Significant examples from algebraic topology
first appeared in the sixties, although the formal definition and
appropriate generality were not forged until the seventies. In the
nineties, a renaissance and further development of the theory were
inspired by the discovery of new relationships with graph
cohomology, representation theory, algebraic geometry, derived
categories, Morse theory, symplectic and contact geometry,
combinatorics, knot theory, moduli spaces, cyclic cohomology, and,
last but not least, theoretical physics, especially string field
theory and deformation quantization. The book contains a detailed
and comprehensive historical introduction describing the
development of operad theory from the initial period when it was a
rather specialized tool in homotopy theory to the present when
operads have a wide range of applications in algebra, topology, and
mathematical physics. Many results and applications currently
scattered in the literature are brought together here along with
new results and insights. The basic definitions and constructions
are carefully explained and include many details not found in any
of the standard literature.
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