C-embedding and the homotopy extension property

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

The joint embedding property and maximal models

We introduce the notion of a ‘pure’ Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show: Main Theorem (cf. Theorem 3.5.2 and Corollary 3.5.6): If 〈λi : i ≤ α < א1〉 is a strictly increasing sequence of characterizable cardinals (Definition 2.1) whose models satisfy JEP(< λ0), there is an Lω1,ω-sentence ψ whose models form a pure AEC...

Homotopy Lie algebras, lower central series and the Koszul property

Let X and Y be finite-type CW–complexes (X connected, Y simply connected), such that the rational cohomology ring of Y is a k–rescaling of the rational cohomology ring of X . Assume H∗(X,Q) is a Koszul algebra. Then, the homotopy Lie algebra π∗(ΩY ) ⊗ Q equals, up to k–rescaling, the graded rational Lie algebra associated to the lower central series of π1(X). If Y is a formal space, this equali...