On C.T.C. Wall’s suspension theorem
- M. A-K Aouina, J. R. Klein
- Forum Mathematicum 18,
Fix K a finite connected CW complex of dimension ≤ k. An n-thickening of K is a pair (M, f) , in which M is a compact n-dimensional manifold and f : K → M is a simple homotopy equivalence. This concept was first introduced by C.T.C. Wall approximately 40 years ago. Most of the known results about thickenings are in a range of dimensions depending on k, n and the connectivity of K. In this paper we remove the connectivity hypothesis on K. We define moduli space of n-thickenings Tn(K). We also define a suspension map E : Tn(K) → Tn+1(K) and compute its homotopy fibers in a range depending only on n and k. We will show that these homotopy fibers can be approximated by certain section spaces whose definition depends only on the choice of a certain stable vector bundle over K.