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5 papers · 2 filters
On embeddings in the sphere
John R. Klein
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
On the homotopy invariance of configuration spaces
Mokhtar Aouina, John R. Klein
For a closed PL manifold M, we consider the configuration space F(M,k) of ordered k-tuples of distinct points in M. We show that a suitable iterated suspension of F(M,k) is a homot…
Motivic cell structures
Daniel Dugger, Daniel C. Isaksen
An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of…
On Kontsevich's Hochschild cohomology conjecture
P. Hu, I. Kriz, A. A. Voronov
Let an n-algebra mean an algebra over the chain complex of the little n-cubes operad. We give a proof of Kontsevich's conjecture, which states that for a suitable notion of Hochsch…
A chain rule in the calculus of homotopy functors
John R. Klein, John Rognes
We formulate and prove a chain rule for the derivative, in the sense of Goodwillie, of compositions of weak homotopy functors from simplicial sets to simplicial sets. The derivativ…