Simple question but I am confused. What is the boundary of $S^2\times\mathbb{R}$? Is it just $S^2$? What would be the general way to evaluate the boundary of a product manifold? Thanks for the replies!

I am physicist. I`ve started studying Topological QFT. What would you recommend to read in mathematical field for understanding Witten’s old articles of 80s-90s? What books/articles could help form proper mathematical background for TQFT?

Could someone give an laymans explanation of the relation between QFT and knot theory? What are the central ideas in Wittens work on the Jones polynomial?

I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are derived: $$ \begin{eqnarray} & {} \quad \int x^{k_1}\cdots x^{k_{2N}} \, \exp\left( – \frac 1 2 \sum_{i,j=1}^{n}A_{ij} x_i x_j \right) \, d^nx \\ & = \sqrt{\frac{(2\pi)^n}{\det […]

This is more of a particle physics question than maths. Since $SO(6)$ and $SU(4)$ are isomorphic, how are the fields (say for example scalar fields of ${\mathcal{N}}=4$ Super Yang Mills in $4d$) transforming under 6 dimensional vector representation of $SO(6)$ related to the fields transforming under antisymmetric 6 of $SU(4)$ ?

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