Displaying similar documents to “An Algebraic Model for G-Simple Homotopy Types.”

Homotopy algebras via resolutions of operads

Markl, Martin

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Summary: All algebraic objects in this note will be considered over a fixed field k of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over k . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [, “La renaissance des opérads”, Sémin. Bourbaki 1994/95, Exp. No....

The equivariant homotopy type of G-ANR's for proper actions of locally compact groups

Sergey A. Antonyan, Erik Elfving (2009)

Banach Center Publications

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We prove that if G is a locally compact Hausdorff group then every proper G-ANR space has the G-homotopy type of a G-CW complex. This is applied to extend the James-Segal G-homotopy equivalence theorem to the case of arbitrary locally compact proper group actions.

Homotopy theory of the master equation package applied to algebra and geometry: a sketch of two interlocking programs

Dennis Sullivan (2009)

Banach Center Publications

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Using the algebraic theory of homotopies between maps of dga's we obtain a homotopy theory for algebraic structures defined by collections of multiplications and comultiplications. This is done by expressing these structures and resolved versions of them in terms of dga maps. This same homotopy theory of dga maps applies to extract invariants beyond homological periods from systems of moduli spaces that determine systems of chains that satisfy master equations like dX + X*X = 0. Minimal...