2007-09-06

WE ARE GOING TO CLASSIFY COMPACT CONNECTED 2-MANIFOLDS!

$\small \noindent To be proved.\par{\sc Theorem.} A compact connected manifold in two dimensions is homeomorphic to one of the following manifolds. \begin{enumerate} \item The 2-sphere. \item A connected sum of $n$ toruses, $\mathop{\#}\limits_1^n T_i$. \item A connected sum of $n$ copies of two-dimensional real projective space, $\mathop{\#}\limits_1^n {\mathbb R}{\mathbb P}^2$. \end{enumerate}$

YAY YAY YAY YAY

My other classes are okay. I have homeworks due.

2007-09-06

(no subject)