As a beginner it’s not very convincing to me still, why K-theory is important. However, the following is interesting to me at least: it seems that the K-groups can be arrived at from a route top down, as opposed to bottom up as we have taken thus far. 884 more words

## Tags » K-theory

#### The Toeplitz Algebra

The Toeplitz algebra is a seeming specific object but apparently has surprisingly far-reaching applications. There are so many minor facts that I’m going to do this in prose form. 435 more words

#### Bott Periodicity

We finally close up the periodicity in Bott periodicity. Like the other parts of the topic, this is extremely technical and long. Let’s jump right into it. 1,169 more words

#### Long Exact Sequence

To finish off Bott periodicity, the next thing we would need to show is that . However, it is useful to go on a slight tangent and discuss the long exact sequence of K-groups. 1,088 more words

#### Suspensions: Linking the First/Zeroth K-groups

It turns out that the periodicity of the K-groups is tied to K-groups of suspensions: the first K-group of a suspension is the zeroth K-group, and vice versa, yielding periodicity. 1,115 more words

#### In Case You Missed It: ALESIA, Brillz, & K Theory Showcase Remixing Prowess

The past few weeks have been so full of music that it was all too easy to miss out on some great songs. Here are three remixes that deserve some more attention: 281 more words