All Questions

The Hauptvermutung proposes the following: if two finite simplicial complexes are homeomorphic then they are PL-homeomorphic, meaning that they have a common refinement. People are mostly interested ...

Fact: The spin cobordism is equivalent to "KO" theory in low dimension if we only consider the 2-torsion. This is related to a question and an answer supports the claim. Here we denote the $p$-...

Can a homotopy domination by a space supporting a free action of $G$ be promoted to a homotopy equivalence with such a space? As stated, this is not a serious question (multiply by an $EG$). But with ...

The main quetion is For a compact Lie group $G$, and a $G$-space $X$ with $K^1(X)=0$. How much can we say about the vanishing of $K_G^1(X)$? Moreover, how much $K^0_G(X)=K^0(X)\times R(G)$? Here $...

Let $K$ be a finite $CW$-complex. Could you give any references or explanations for the following two items? I do not understand. Thanks! (1). The Chern character from $\tilde{KO}^0(K)$ to the ...

Let $B$ be a finite CW-complex and $\xi$ be a vector bundle over $B$ with structure group $\Sigma_n$, the $n$-th symmetric group. Then corresponding to $\xi$, we have a classifying map $$ g\in \tilde {...