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A Swashbuckling Tour of Elliptic Cohomology
In singular cohomology, the first chern class of two tensored line bundles $c_1( A \otimes B) = c_1(A) + c_1(B)$ is the additive formal group law, $F(x,y) = x + y$. Quillen was messing with K-theory...
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The Landweber exact-functor theorem
This post assumes familiarity with formal group laws, the definition of exact sequences, the motivation of the Landweber-Ravenel-Stong construction, that the exactness axioms is one of the generalized...
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Landweber-Ravenel-Stong Construction Flowchart
Here’s a flowchart I made while preparing for an upcoming talk. I fear that it may be hard to follow without being already familiar with the story, but there’s little harm in posting it. Maybe it’ll...
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What does the sphere spectrum have to do with formal group laws?
This post assumes that you’re familiar with the definition of a prime ideal, a local ring, $R_{(p)}$, the sphere spectrum, $\mathbb{S}$, and the Lazard ring, $L$. During a talk Jacob Lurie gave at...
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A First Look at an Equivariant Elliptic Cohomology
Usually, besides the information preserved by the formal group law of the elliptic curve, we can’t see any information about the elliptic curve when looking at the output of its associated cohomology...
View ArticleCalculating $\pi_*(tmf)$ at the prime 2
I wrote my Master’s thesis. It is an illustrated Guide to using the May spectral sequence. a1 If the pdf viewer doesn’t work, here is a link to the paper.
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