عنوان

Simplicial and operad methods in algebraic topology /

0821821709 (acid-free paper)

9780821821701 (acid-free paper)

dltt

Simplicial and operad methods in algebraic topology /

[Book]

V.A. Smirnov.

Providence, R.I. :

American Mathematical Society,

c2001.

x, 235 p. ;

27 cm.

Translations of mathematical monographs,

v. 198

0065-9282 ;

Includes bibliographical references (p. 231-232) and index.

Operads in the Category of Topological Spaces -- A[infinity]-structure on a loop space -- Operads and spaces over operads -- Little cubes operads and loop spaces -- Operads and monads -- Bioperads in the category of topological spaces -- Simplicial Objects and Homotopy Theory -- Simplicial and cosimplicial objects -- Simplicial sets -- A[infinity]-simplicial objects and A[infinity]-topological groups -- Homotopy type and A[infinity]-group structure -- Algebraic Structures on Chain Complexes -- Chain complexes -- Algebras and modules over an algebra -- Twisted tensor products and functor D -- Bar constructions and cobar constructions -- Lie modules and comodules -- [logical or]-algebras and [logical and]-coalgebras -- A[infinity]-Structures on Chain Complexes -- A[infinity]-algebras and A[infinity]-coalgebras -- A[infinity]-modules and A[infinity]-comodules -- A[infinity]-[logical or]-algebras and A[infinity]-[logical and]-coalgebras -- Commutative A[infinity]-algebras and A[infinity]-coalgebras -- The functor D for A[infinity]-algebras -- Operads and Algebras over Operads -- Operads in the category of chain complexes -- Algebras and coalgebras over operads -- E[infinity]-structure on cobar constructions -- Bar constructions on operads -- Bar constructions on algebras over operads -- Homology and cohomology of an E[infinity]-operad -- Homology of Iterated Loop Spaces -- Chain complex of an iterated loop space -- Computation of the second term of the spectral sequence of iterated loop spaces.

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Simplit͡sialʹnye i operadnye metody v algebraicheskoĭ topologii.

English

Algebraic topology.

Operads.

Ordered algebraic structures.

Smirnov, V. A., (Vladimir Alekseevich),1949-

20140220045132.0

[Book]

Y