Embedding proper homotopy types

A Simplicial Model for Proper Homotopy Types

The singular simplicial set Sing(X) of a space X completely captures its weak homotopy type. We introduce a category of controlled sets, yielding simplicial controlled sets, such that one can functorially produce a singular simplicial controlled set CSing(MaxCtl(X)) from a locally compact X. We then argue that this CSing(MaxCtl(X)) captures the (weak) proper homotopy type of X. Moreover, our te...

Homotopy Types

For an arbitrary simplicial complex K, Davis and Januszkiewicz have defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to Davis and Januszkiewicz’s examples. It is therefore natural to investigate t...

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

TQFTs from Homotopy n-types

Using simplicial methods developed in 22], we construct topological quantum eld theories using an algebraic model of a homotopy n-type as initial data, generalising a construction of Yetter in 23] for n=1 and in 24] for n=2