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 …

Background Model categories are an axiomization of the machinery underlying the study of topological spaces up to homotopy equivalence. They consist of a category $C$, together w …

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 bu …

The theory of Clifford algebras gives us an explicit lower bound for the number of linearly independent vector fields on the $n$-sphere, and Adams proved that this is actually alwa …

This question is on "computing" the Grothendieck group of the projective $n$-space with $m$ origins ($m\geq 1$). For any (noetherian) scheme $X$, let $K_0(X)$ be the Grothendieck g …

As I mentioned in my previous post, I am studying the article Moduli of Enriques surfaces and Grothendieck-Riemann-Roch. The Grothendieck-Riemann-Roch theorem is applied there to …

We look at a familiy $D_\alpha$ of Dirac operators over a (compact) base space B. The projection $\Pi^+_\alpha$ onto the positive eigenspaces of $D_\alpha$ is usually not continuou …

Morel and Voevodsky construct the motivic stable homotopy category, a category through which all cohomology theories factor and where they are representable, by starting with a cat …

Given a finite CW complex X, there is a filtration of the topological K-theory of X given by setting $K_n(X) = \ker \left(K(X) \to K(X^{(n-1)})\right)$, where $X^{(n-1)}$ is the (n …

Hi, I came across the space $BU_\otimes$ when struggling with twisted K-theory. Segal proved that this is an H-space, right? I have read a dozen times by now that the group $[X, …

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 classific …

K-theory sits in an intersection of a whole bunch of different fields, which has resulted in a huge variety of proof techniques for its basic results. For instance, here's a scatt …

I apologize that this is perhaps not adequate for mathoverflow but I have struggled with this for days now and become desperate... The reduced K-group $\tilde{K}(S^0)$ of the zero …

It might be a stupid question. When I took a look at the definition of Q-construction. It makes for an exact category $P$, one defines a new category $QP$ whose objects are the s …

Theorem 3.2 of the paper "Quantum cohomology of the Springer resolution" by Braverman, Maulik and Okounkov relates equivariant quantum cohomology of the cotangent bundle of $G/B$ …