/sci/ - Science & Math

>>4604775
that looks fine for b, although it's a bit dirty and doesn't really state what you're doing. i don't know why you're introducing <span class="math">|\partial s_{x}| > |\bar{\partial} s_{x}|[/spoiler] without explaining such first. it's pretty elegant to use the mapping <span class="math">\nabla s_{x} : T_{x} M \to L_{x}[/spoiler], though. ...is <span class="math">x \in Z[/spoiler]?


your proof doesn't at all handle a. for that you need to deal with <span class="math">\nabla s(u)[/spoiler]. you could do this by proving the graph has transversality to its lagrangian subspace which would give you the smoothness you need (think of vectors in <span class="math">T_{x} M[/spoiler]). you can then find the tangent space with simple set intersections to this graph.

>>4604389
what? do you even know what a harmonic form is? this would do absolutely nothing, there's no application to morse/hodge theory in here...

>not think string/M-theory are particularly mathematically elegant
how so? AdS/CFT, supergravity, and the incorporation of <span class="math">E_{8}[/spoiler] are some of the most beautiful pieces of mathematics i've ever seen.