All Questions

I am reading a paper which uses some $K$-homology which is the homology theory dual to $K$-theory can be defined using the homotopy theoretic formulation: $$ K_\ast(X)\cong\pi_\ast(K\wedge X). $$ ...

$$ \newcommand{\mc}[1]{\mathcal{#1}} \newcommand{\mbb}[1]{\mathbb{#1}} \newcommand{\opn}[1]{\operatorname{#1}} \DeclareMathOperator\cap{cap} \def\sse{\subseteq} $$ Coarse spaces Let $X$ be a coarse ...

Let $M$ b a closed connected smooth manifold with fundamental group $\Gamma$. Suppose $G$ is a simply-connected Lie group that acts smoothly on $M$. Then the Borel construction $$M//G = M \times_G EG$$...

Let me recall the conjecture: $M$ and $N$ two aspherical closed $n$-manifolds with isomorphic fundamental groups, then $M$ and $N$ are homeomorphic.

The Artin braid groups $B_n$ and the symmetric groups $S_n$ are closely related by the maps $1 \to P_n \to B_n \to S_n \to 1$. The infinite symmetric group has interesting interactions with homotopy ...