A germline T-cell receptor variable region (V beta) gene segment (V beta 14) has been mapped 10 kilobases to the 3' side of the constant region (C beta 2) gene. The V beta 14 gene segment is in an inverted transcriptional polarity relative to the diversity-region (D beta) and joining-region (J beta) gene segments and the C beta genes. Analyses of a T-cell… (More)
We review Quillen's concept of a model category as the proper setting for deening derived functors in non-abelian settings, explain how one can transport a model structure from one category to another by mean of adjoint functors (under suitable assumptions), and deene such structures for categories of cosimplicial coalgebras. 1. Introduction Model… (More)
We provide a general definition of higher homotopy operations, encompassing most known cases, including higher Massey and Whitehead products, and long Toda brackets. These operations are defined in terms of the W-construction of Board-man and Vogt, applied to the appropriate diagram category; we also show how some classical families of polyhedra (including… (More)
We define a sequence of purely algebraic invariants – namely, classes in the Quillen cohomology of the Π-algebra π * X – for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract Π-algebra can be realized as the homotopy Π-algebra of a space.
Given a diagram of …–algebras (graded groups equipped with an action of the primary homotopy operations), we ask whether it can be realized as the homotopy groups of a diagram of spaces. The answer given here is in the form of an obstruction theory, of somewhat wider application, formulated in terms of generalized …–algebras. This extends a program begun by… (More)
We describe an obstruction theory for a given topological space X to be an H-space, in terms of higher homotopy operations, and show how this theory can be used to calculate such operations in certain cases.
We show how a certain type of CW simplicial resolutions of spaces by wedges of spheres may be constructed, and how such resolutions yield an obstruction theory for a given space to be a loop space.
Given a suitable functor T : C → D between model categories, we define a long exact sequence relating the homotopy groups of any X ∈ C with those of T X, and use this to describe an obstruction theory for lifting an object G ∈ D to C. Examples include finding spaces with given homology or homotopy groups. A number of fundamental problems in algebraic… (More)