Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Trace amounts of torsion found

It is a classical result that a simple homotopy type (i.e. a CW-complex up to simple homotopy equivalence) can be algebraically given by the underlying homotopy type together with an algebraic invariant Reidemeister/Whitehead-torsion living in K-theory. Using the Dennis trace map from K-theory to Hochschild-homology we can formally define an analogous notion. We will discuss this notion in the case of manifolds. More precisely, we will show that the resulting structure allows one to define a relative intersection product, which can also be extracted from the configuration space of two points. On one hand, this gives a recipe to extract the trace of the Whitehead torsion from the configuration space of two points, and on the other hand explains why the string coproduct is not homotopy invariant. This is joint work with Pavel Safronov.