3,736 research outputs found
Models for classifying spaces and derived deformation theory
Using the theory of extensions of L-infinity algebras, we construct rational
homotopy models for classifying spaces of fibrations, giving answers in terms
of classical homological functors, namely the Chevalley-Eilenberg and Harrison
cohomology. We also investigate the algebraic structure of the
Chevalley-Eilenberg complexes of L-infinity algebras and show that they
possess, along with the Gerstenhaber bracket, an L-infinity structure that is
homotopy abelian.Comment: 23 pages. This version contains minor technical corrections and a new
section with a list of open problems. To appear in Proceedings of the LM
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
The Stasheff model of a simply-connected manifold and the string bracket
We revisit Stasheff's construction of a minimal Lie-Quillen model of a
simply-connected closed manifold using the language of infinity-algebras.
This model is then used to construct a graded Lie bracket on the equivariant
homology of the free loop space of minus a point similar to the
Chas-Sullivan string bracket.Comment: 9 page
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