Recall that complex $K$-theory is a cohomology theory on topological spaces, which can be described in several equivalent ways: Given a finite complex $X$, $K^0(X)$ is the Groth …

I'll begin with some background that is unnecessary for the actual question, but that might be interesting to the reader: Topological modular forms ($TMF$) is a generalized cohomo …

Let M be a closed spin manifold of dimension $d$. One form of the elliptic genus of $M$ is $$ F(q)=q^{-d/8} \hat A(M) {\rm ch} \otimes_{k=1/2,3/2,\cdots} \Lambda_{q^k}T \otimes_{\ …

What is a topological modular form? How are they related to 'normal' (number-theoretic) modular forms?

I'm trying to understand better the mathematical notion of elliptic cohomology. Note that I only know the physics definition of the elliptic genus given in Witten's paper. Let $X …

Reading Ravenel's "green book", I wonder about his question on p.15 "that the spectrum MU may be constructed somehow using formal group law theory without using complex manifolds o …