Homogenization of differential operators
Summary: All algebraic objects in this note will be considered over a fixed field of characteristic zero. If not stated otherwise, all operads live in the category of differential graded vector spaces over . For standard terminology concerning operads, algebras over operads, etc., see either the original paper by J. P. May [“The geometry of iterated loop spaces”, Lect. Notes Math. 271 (1972; Zbl 0244.55009)], or an overview [J.-L. Loday, “La renaissance des opérads”, Sémin. Bourbaki 1994/95,...
The paper is concerned with homotopy concepts in the category of chain complexes. It is part of the author’s program to translate [J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lect. Notes Math. 347, Springer-Verlag (1973; Zbl 0285.55012)] from topology to algebra.In topology the notion of operad extracts the essential algebraic information contained in the following example (endomorphism operad).The endomorphism operad of a based space consists...
Let denote the configuration space of pairwise-disjoint -tuples of points in . In this short note the author describes a cellular structure for when . From results in [F. R. Cohen, T. J. Lada and J. P. May, The homology of iterated loop spaces, Lect. Notes Math. 533 (1976; Zbl 0334.55009)], the integral (co)homology of is well-understood. This allows an identification of the location of the cells of in a minimal cell decomposition. Somewhat more detail is provided by the main result here,...
This paper describes I2Geo, the platform of the Intergeo project enabling math educators throughout Europe to publicly share interactive geometry constructions. This cross-cultural web-based platform makes each resource, be it a construction, a scenario of use, or a complete course, referenceable, editable, and reviewable. It is based on reusable tools, a fine grained ontology of mathematical concepts and skills, together with a description of educational pathways in Europe: together they allow...