Embedding homotopy cells

Embedding , Compression and Fiberwise Homotopy

Embedding , compression and berwise homotopy theory

Given Poincar e spaces M and X , we study the possibility of compressing embeddings of M I in X I down to embeddings of M in X . This results in a new approach to embedding in the metastable range both in the smooth and Poincar e duality categories. AMS Classi cation 57P10; 55R99

Embedding, Compression and Fiberwise Homotopy Theory

Given Poincaré spaces M and X , we study the possibility of compressing embeddings of M×I in X×I down to embeddings of M in X . This results in a new approach to embedding in the metastable range both in the smooth and Poincaré duality categories. AMS Classification 57P10; 55R99

A Homotopy-theoretic Proof of Williams’s Metastable Poincaré Embedding Theorem

Recall the notion due to W. Browder of a Poincaré embedding [Br1, Br3, Br2, Br4, Wa, Ra, Wi1, Wi2], which is the homotopy analogue of a smooth embedding of manifolds. Let (M,A) be a simply connected m-dimensional (finite) Poincaré pair. A Poincaré embedding of (M,A) in the sphere S will mean a finite CW-complex W and a map f : A −→ W , such that the homotopy pushout M ∪ι A× [0, 1] ∪f W is homot...

Homotopy Theory of Homotopy Algebras

The goal of this paper is to study the homotopy theory of homotopy algebras over a Koszul operad with their infinity morphisms. The method consists in endowing the category of coalgebras over the Koszul dual cooperad with a model category structure. CONTENTS Introduction 1 1. Recollections 2 2. Model category structure for coalgebras 5 3. Conclusion 14 Appendix A. A technical lemma 15 Reference...