5
votes
1answer
193 views

What is the ring structure of the complex topological K-theory of a non-singular complex quadric?

I would like to know the ring structure of $K(Q_n)$ explicitly where $Q_n \subset \mathbb{P}^{n+1}$ is the non-singular $n$-dimensional complex quadric and $K(Q_n) = K^0(Q_n)$ is the complex ...
0
votes
2answers
115 views

free complex with mod-p coefficients

How does one prove the following fact. I could not find anything in literature. Let $\pi$ be a subgroup of the symmetric group $S_p$ and let $W$ be a free $\pi$-complex. Then for any space $X$ there ...
10
votes
1answer
436 views

Homology of infinite loop spaces $QX$

Let $X$ be a simply connected space. By $Q$ I denote $\Omega^{\infty}\Sigma^{\infty}$. Then $QX$ is an infinite loop space and the homology $H(QX)$ in $\mathbb{F}_p$ is a Hopf algebra over the ...
2
votes
1answer
343 views

Spectral sequence for H-space bundles

Let $F \rightarrow E \rightarrow B$ be a fibre bundle such that $B$ is a smooth and compact manifold and $F$ obtains an associative H-space structure. Explicitly, it is not a principal bundle. One ...
10
votes
3answers
930 views

Is there a good definition of (topological) K-Theory over arbitrary spaces?

Hi (this is my very first question here, so please don't hurt me...) for some time now i've been looking for a sufficiently aesthetical definition of (topological) K-theory of arbitrary spaces, yet ...
6
votes
0answers
263 views

homotopy domination that splits a non-split epimorphism and still wants to be a homotopy equivalence

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 ...
6
votes
1answer
991 views

K-theory as a generalized cohomology theory

Which of the statements is wrong: a generalized cohomology theory (on well behaved topological spaces) is determined by its values on a point reduced complex $K$-theory $\tilde K$ and reduced real ...
6
votes
2answers
313 views

Relation between $KO$ and $K$

What can be said about the relation between the complex and the real K-theory of a CW complex? An $n$-dimensional complex vector bundle is an $2n$-dimensional real vector bundle but not vice versa. ...
6
votes
1answer
493 views

Freedman's work on non-simply-connected 4-manifolds

In the late 1970's and in the 1980's, Michael Freedman showed a relationship between the topological surgery problem in 4-dimensions, the slice problem for links, and the classification of ...