Sep. 6th, 2007

(no subject)

Sep. 6th, 2007 07:46 pm
synchcola: (heyoka "ok")
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.
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synchcola

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