Algebra Seminar 

17/04/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Lucile Vandembroucq, Universidade do Minho, Braga

Embeddings up to homotopy of a CW-complex in a sphere

We say that a finite CW-complex $X$ embeds up to homotopy in a sphere $S^n$ if there exists a subpolyhedron $K\subset S^n$ having the same homotopy type as $X$. In this talk, I will explain a sufficient condition for the existence of such an embedding in a given codimension that we obtained in the particular case where $X$ is a two-cone (that is, $X$ is the homotopy cofibre of a map between two suspensions). As an application of this result, we will see that there is no rational obstruction to embeddings up to homotopy of a two-cone in codimension 3.

(joint work with P. Lambrechts and D. Stanley)