All Questions

Let us assume that $f:X \to Y$ is a map of connected CW complexes, having the following property: if $K$ is a finite CW complex, then the induced map $f_{\ast}:[K,X] \to [K,Y]$ on \emph{free} homotopy ...

Is it possible to construct a theory of fundamental groups $\pi_1 (A,a_0)$ for pointed $C^*$-algebras $(A,a_0)$ instead of pointed topological spaces $(X,x_0)$ : $\pi_0 (X,x_0)$ ? If the answer is yes,...

Suppose that $X, B$ are smooth irreducible varieties over $\mathbb{C}$ and $f : X \to B$ is a smooth proper morphism. Then we can consider the homotopy exact sequence: $$ \pi_2(B) \to \pi_1(F) \to \...