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- 19:33, 22 November 2013 11-19 Notes (hist) [6,523 bytes] Vanabel (Talk | contribs) (Created page with "section{Uhlenbeck's lemma:$L^n$ estimates: Continued} Recall the notation $\mathcal A_1^p$, $n/2< p< n$, $\pt X$ maybe nonempty, $S_A(\eps)=\set{A+a|\rd_A^* a=0,*a|_{\pt X}=0,...")
- 19:33, 22 November 2013 11-17 Notes (hist) [4,839 bytes] Vanabel (Talk | contribs) (Created page with "\section{Uhlenbeck's lemma:$L^n$ estimates} Let $E$ be a vector bundle over $M^n$ with fiber $\C^d$. Fix a $\C^\infty$ connection $A$ in $\mathcal A_1^{n/2^*}$, set $S_A(\eps)...")
- 19:30, 22 November 2013 11-12 Notes (hist) [4,377 bytes] Vanabel (Talk | contribs) (Created page with " \section{Uhlenbeck's Lemma: Continued} \begin{lem}[Uhlembeck's Lemma] Suppose $n\leq4$, then there exists $\eps$, $C >0$, such that if $A\in L_1^2(B^n,\wedge^1\otimes g)$ and...")
- 13:28, 17 December 2008 12-08 Notes (hist) [2,226 bytes] Andy (Talk | contribs) (Section 1)
- 01:03, 16 December 2008 12-10 Notes (hist) [2,200 bytes] TimN (Talk | contribs) (New page: TESTING $f(x) = \sum$)
- 15:22, 14 December 2008 10-08 Notes (hist) [6,691 bytes] Nikhilas (Talk | contribs) (New page: \section{Generators for cohomology of $B\mathcal{G}$} Following the previous lecture the goal is to identify generators for the cohomology of $B\mathcal{G} = \text{Map} [\Sigma , BU_n]$....)
- 22:00, 12 December 2008 10-22 Notes (hist) [6,378 bytes] Sthilai (Talk | contribs) (New page: Morse theory allows us to determine topological and geometric properties of manifolds by studying the critical points of special real-valued functions known as Morse functions.Marston Mors...)
- 10:19, 10 December 2008 09-10 Notes (hist) [11,011 bytes] Tatyanak (Talk | contribs) (New page: \begin{document} \title{MIT Geometry Seminar \\ Lecture 3 \\ 9/10/2008} \maketitle Let $X$ be a compact Riemanian manifold, and $P$ be a principal bundle over $X$ with structure group...)
- 13:17, 9 December 2008 11-05 Notes (hist) [5,122 bytes] Lu (Talk | contribs) (New page: \section{Uhlenbeck Gauge Fixing Lemma} Let $A(t)$ be a solution to $\frac{\partial A}{\partial t}=D^*_AF_A$ and thus $\mathcal{E}(A(t_1))-\mathcal{E}(A(t_0))= \int_{t_1}^{t_0}\norm{D^*_AF...)
- 14:29, 4 December 2008 10-29 Notes (hist) [14,285 bytes] Djhanen (Talk | contribs) (New page: Claiming page; I'll write it this weekend.)
- 23:27, 1 December 2008 11-24 Notes (hist) [7,230 bytes] Ssivek (Talk | contribs) (This is a draft of my notes from lecture 21.)
- 17:46, 30 November 2008 10-27 Notes (hist) [5,053 bytes] Bsingh (Talk | contribs) (New page: \section{Morse-Bott Functions} \begin{defn} Let $f:M\rightarrow \mathbb{R}$ be a smooth function. We say that $f$ is Morse-Bott if the critical set $C=\{x\in M|d_x f=0\}$ can be writtin ...)
- 15:05, 25 November 2008 09-24 Notes (hist) [6,053 bytes] Lu (Talk | contribs) (New page: \maketitle \section{Injectivity} Suppose that $A\in \mathcal{A}^p_k$ and $(k+1)p>n$. For $\forall \epsilon>0$, define \begin{equation} S_{A,\epsilon}=\{A+a|\ d_A^*a=0,\ \norm{a}_{L^p_k}<...)
- 16:56, 13 November 2008 09-03 Notes (hist) [11,644 bytes] Sthilai (Talk | contribs) (New page: These lecture notes are based on notes from the 18.999 geometry seminar class taught by Tomasz Mrowka and from the IAS/Park city Mathematic series book ''Gauge theory and the topology of...)
- 19:36, 12 November 2008 09-08 Notes (hist) [7,842 bytes] Bsingh (Talk | contribs) (New page: \newcommand{\e}{\epsilon} \newcommand{\ra}{\rightarrow} \newcommand{\g}{\mathfrak{g}} \newcommand{\M}{\mathcal{M}} \newcommand{\al}{\alpha} \newcommand{\PR}{\mathcal{P}} \newcommand{\Q}{\m...)
- 12:21, 12 November 2008 10-20 Notes (hist) [7,998 bytes] Afr (Talk | contribs) (New page: == Review of the notation == $\C^2 \to E \to \Sigma$ with $\det E = \Delta$ and $<c_1(\Delta),[\Sigma]> =1$ $A \in \mathcal{A}_{\delta} = \{ A \in \mathcal{A}_E: \det A = \delta \}$ $\m...)
- 11:29, 12 November 2008 09-29 Notes (hist) [10,472 bytes] Afr (Talk | contribs) (New page: \noindent\textbf{Brief Recap.}\\ $P\to M$ unitary frame bundle of a vector bundle $E\to M$.\\ Yang-Mills functional: $\mathcal{E}(A)=\int_M |F_A|^2=\int_{M} -\textrm{tr}(F_A \wedge *F_A)$....)
