منابع مشابه
Brace Bar-cobar Duality
Using Kadeishvili’s [11] formulas with appropriate signs, we show that the classical cobar construction from coalgebras to algebras Ω : CoAlg → Alg can be enhanced to a functor from Hopf algebras to E2 algebras (for a certain choice of E2 operad) Ω : HopfAlg → E2Alg, which, unlike its classical counterpart, is not strictly adjoint, but homotopically equivalent to the left adjoint of the enhance...
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We prove that for any 1-reduced simplicial set X, Adams’ cobar construction ΩCX on the normalised chain complex of X is naturally a strong deformation retract of the normalised chains CGX on the Kan loop group GX. In order to prove this result, we extend the definition of the cobar construction and actually obtain the existence of such a strong deformation retract for all 0-reduced simplicial s...
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This paper is a contribution to the study of Borel equivalence relations on standard Borel spaces (i.e., Polish spaces equipped with their Borel structure). In mathematics one often deals with problems of classification of objects up to some notion of equivalence by invariants. Frequently these objects can be viewed as elements of a standard Borel space X and the equivalence turns out to be a B...
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These are lecture notes from a minicourse given at Louvain-laNeuve in May 2007. There is a high, but not perfect, correlation between the contents of these notes and the subjects covered in the minicourse. Note that since these are lecture notes and not an article, many proofs are not included, while those that are included are only sketches, which are particularly brief when the proofs have al...
متن کاملAdams, H
Experiments were performed to determine the effect of community composition on system function (bacterial production) in arctic Alaska. In this system bacterial production is controlled by: community, temperature, nutrients, and carbon source. Lake inlet and outlet communities in these experiments were different in composition, based on PCR-DGGE fingerprinting of 16S rDNA. For both communities,...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1992
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1992-1036001-2