View source for User talk:Harold

== A collection of thoughts on Morse theory ==

I'm currently trying to figure out why in Morse homology, the degree of the attaching map of a certain <m>n</m>-cell is somehow equivalent to the number of gradient flow lines.
The setup is as following. Let <m>(M, g)</m> be a closed (i.e., compact and connected) smooth Riemannian manifold (without boundary), and suppose <m>f: M \to \mathbb{R}</m> is a smooth map satisfying the following properties:
# for each <m>x \in \mathrm{Crit}(f) := { p \in M : df_p = 0 }</m>, the Hessian <m>\mathrm{Hess}(f): T_pM \times T_pM \to \mathbb{R}</m> is non-degenerate. '''TODO Define the Hessian.'''
# <m>f|_{\mathrm{Crit}(f)}: \mathrm{Crit(f)} \to \mathbb{R}</m> is injective.

== Caveat with xymatrix ==

Hey, try this page:
* [[/Xymatrix caveat]]
See how you can scroll right? [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:08, 14 February 2017 (UTC)

== Some copy-and-paste-help ==

It's good to render diagrams in tables, if only because they look a bit sparse with the white background (unless they're huge), try these:
{| class="wikitable" border="1" style="overflow:hidden;max-width:35em;"
|-
| <center><span style="font-size:1.2em;"><mm>\text{YOUR MATH HERE}</mm></span></center>
|-
! Comment
|}
To float to the right:
<div style="float:right;margin:0px;margin-left:0.2em;">
{| class="wikitable" border="1" style="overflow:hidden;max-width:35em;margin:0px;"
|-
| <center><span style="font-size:1.2em;"><mm>\xymatrix{A \ar[r]^f & B}</mm></span></center>
|-
! Comment
|}
</div>Now you can write here and reference the diagram on the right
* Lists and everything
** Baby
Hope it helps [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 22:15, 14 February 2017 (UTC)