2
votes
2answers
162 views

Preimage of $1 \in H^n(M^n)$ under Chern character

Let $M$ be a closed, oriented manifold of dimension $n$. We know that the Chern character induces an isomorphism $K^\ast(M) \otimes \mathbb{Q} \cong H^\ast(M; \mathbb{Q})$ and now I was wondering how ...
13
votes
2answers
1k views

Does a “Chern character” exist for any generalized cohomology theory?

The Chern character is a ring homomorphism from the complex K-theory to the usual cohomology. 1) I wonder if there are "Chern character"-like ring homomorphisms from other generalized cohomology ...