MathOverflow

I am looking for a book/monograph which deals with superconformal (vertex operator) algebras and their representation theory. What are some good books to understand to begin with the definition of a vertex operator superalgebra and then go to superconformal...

I've been working on this for almost a year now & I've hardly made progress. Should I give up?

Define $K_n (A)$ to be $\pi_{n-1}$ of the simplicial group $GL(A*{\mathbb Z} \{t_0,…,t_n\}/(t_0+…+t_n-1))$. Here ${\mathbb Z}\{t_0,…,t_n\}$ denotes the free algebra. Does this compute the Quillen K-theory of A?

Let $(M, g)$ be a closed smooth riemannian manifold and consider a solution to the Allen--Cahn equation
$$\Delta_g u = u(u^2 - 1)$$
which I will rewrite as $L_u(u) = 0$ for $L_u = \Delta_g + (1 - u^2)$ (i.e. the laplacian plus a potential). Moreover we can assume $|u| < 1$ everywhere....