/sci/ - Science & Math

>>9607061
>So if we are constructing tangent spaces, this implies the moduli space is more than just a topological space right?
Yes. It's an infinite-dimensional vector bundle. Regarding what I said before about Euler characteristics, in certain cases the Yang-Mills path integral is a generalization of the Euler characteristics to infinite-dimensions via Mathai-Quillen.
>It has some type of analytic or algebraic structure?
Mostly algebraic, from the structure group [math]G[/math]. But if you want to look at matter fields coupled with the gauge fields then you'd need a lot more analytic structure (Swieca regularity, say) for a well-defined QFT.