000			03089cam a2200277 i 4500
001			136738
003			ISI Library, Kolkata
005			20160407154513.0
008			141218s2015 riua b 001 0 eng
020			_a9781470421977 (hardback: alk. paper)
040			_aISI Library _beng
082	0	4	_a510MS _223 _bAm512
100	1		_aYau, Donald.
245	1	0	_aFoundation for PROPs, algebras, and modules / _cDonald Yau and Mark W. Johnson.
260			_aProvidence : _bAmerican Mathematical Society, _c2015.
300			_axxxi, 311 p. : _billustrations ; _c26 cm.
490	0		_aMathematical surveys and monographs ; _vv 203.
504			_aIncludes bibliographical references and index.
505	0		_aPart 1. Wheeled graphs and pasting schemes. 1. Wheeled graphs -- 2. Special sets of graphs -- 3. Basic operations on wheeled graphs -- 4. Graph groupoids -- 5. Graph substitution -- 6. Properties of graph substitution -- 7. Generators of graphs -- 8. Pasting schemes -- 9. Well-matched pasting schemes -- Part 2. Generalized PROPs, algebras, and modules. 10. Generalized PROPs -- 11. Biased characterizations of generalized PROPs -- 12. Functors of generalized PROPs -- 13. Algebra over generalized PROPs -- 14. Alternative descriptions of generalized PROPs -- 15. Modules over generalized PROPs -- 16. May modules over algebras over operads -- Bibliography -- Index.
520			_aPROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs. Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero. This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.
650		0	_aPermutation groups.
650		0	_aCategories (Mathematics)
650		0	_aModules (Algebra)
700	1		_aJohnson, Mark W., _eauthor
942			_2ddc _cBK
999			_c420768 _d420768