1,996 research outputs found
Towers of MU-algebras and the generalized Hopkins-Miller theorem
Our results are of three types. First we describe a general procedure of
adjoining polynomial variables to -ring spectra whose coefficient
rings satisfy certain restrictions.A host of examples of such spectra is
provided by killing a regular ideal in the coefficient ring of MU, the complex
cobordism spectrum. Second, we show that the algebraic procedure of adjoining
roots of unity carries over in the topological context for such spectra. Third,
we use the developed technology to compute the homotopy types of spaces of
strictly multiplicative maps between suitable K(n)-localizations of such
spectra. This generalizes the famous Hopkins-Miller theorem and gives
strengthened versions of various splitting theorems
Abstract Hodge decomposition and minimal models for cyclic algebras
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy
Feynman diagrams and minimal models for operadic algebras
We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras
Cocommutative coalgebras: homotopy theory and Koszul duality
We extend a construction of Hinich to obtain a closed model category
structure on all differential graded cocommutative coalgebras over an
algebraically closed field of characteristic zero. We further show that the
Koszul duality between commutative and Lie algebras extends to a Quillen
equivalence between cocommutative coalgebras and formal coproducts of curved
Lie algebras.Comment: 38 page
Automatic processing system for shadowgraph and interference patterns
The design and operation of an automatic system for the processing of shadowgraph and interference images are described. The system includes a two-coordinate processing table with an optical system for the projection of transparent images onto the photodetector, an image filter in the photodetector field, and a device for controlling the movement of the table and transmitting information to the minicomputer
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Cocommutative coalgebras: homotopy theory and Koszul duality
We extend a construction of Hinich to obtain a closed model category structure on all differential graded cocommutative coalgebras over an algebraically closed field of characteristic zero. We further show that the Koszul duality between commutative and Lie algebras extends to a Quillen equivalence between cocommutative coalgebras and formal coproducts of curved Lie algebras
Koszul-Morita duality
We construct a generalization of Koszul duality in the sense of Keller-Lefèvre for not necessarily augmented algebras. This duality is closely related to classical Morita duality and specializes to it in certain cases
Homology and Cohomology of E-infinity Ring Spectra
Every homology or cohomology theory on a category of E-infinity ring spectra
is Topological Andre-Quillen homology or cohomology with appropriate
coefficients. Analogous results hold for the category of A-infinity ring
spectra and for categories of algebras over many other operads
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