The metastable homotopy of $O\left( n \right)$

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...

n-RELATIVE CATEGORIES: A MODEL FOR THE HOMOTOPY THEORY OF n-FOLD HOMOTOPY THEORIES

We introduce, for every integer n ≥ 1, the notion of an n-relative category and show that the category of the small n-relative categories is a model for the homotopy theory of n-fold homotopy theories, i.e. homotopy theories of . . . of homotopy theories. 1. Background and motivation In this introduction we • recall some results of (higher) homotopy theory, and • explain how they led to the cur...

ON THE HOMOTOPY THEORY OF n-TYPES

We achieve a classification of n-types of simplicial presheaves in terms of (n− 1)-types of presheaves of simplicial groupoids. This can be viewed as a description of the homotopy theory of higher stacks. As a special case we obtain a good homotopy theory of (weak) higher groupoids.

Right gw-Majorization on M_{n,m}

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