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--- math214:home [2020/04/24 13:54]
pzhou [Lectures]
+++ math214:home [2020/12/18 21:23] (current)
pzhou
@@ Line 115: / Line 115: @@
     * typo in the note: one page 2, right column. I wrote incorrectly that, "if $p \in K \cap gK$ then $p, gp \in K$". The correct statement is that  "if $g \in G_K$, then there exist $p \in K$ such that $g \cdot p \in K$".
   * 03-20: Ch 19, Distribution. covered up to Frobenius Thm (statement and sketch of proof)
-    * HW9: Ch 21: 1,5,9,16. Ch 19: 1.
+    * HW9: Ch 21: 1,5,9,16. Ch 19: 1. [[hw9-sol]]
   * Week 10. From Wednesday on, we will start to use the [[https://www3.nd.edu/~lnicolae/Lectures.pdf| lecture note of Nicolascu ]] for topics about connections, denoted as [Ni]
     * 03-30: Riemannian metric: an introduction with examples and no proofs.[Lee]
@@ Line 125: / Line 125: @@
   * Week 11:
     * [[04-06]]: {{ :math214:note_6_apr_2020.pdf |ipad note}}Holonomy, interpretation of Curvature[Ni] 3.3.4
-      * Errata of ipad note: page 1, right column. It should be: if $A = \omega \ot (e_\alpha \ot \delta^\beta)$, for $\omega \in \Omega^1(U)$ and $e_\alpha$ the local frame of $E$ previously chosen, and $\delta^\beta$ the dual frame of $E^*$, then $dA = d(\omega) \ot (e_\alpha \ot \delta^\beta)$. This is because $d e_\alpha =0, d \delta^\beta=0$ by the definition of local connection $d$ on $E|_U$.
+      * Errata of ipad note: page 1, right column. It should be: if $A = \omega \otimes (e_\alpha \ot \delta^\beta)$, for $\omega \in \Omega^1(U)$ and $e_\alpha$ the local frame of $E$ previously chosen, and $\delta^\beta$ the dual frame of $E^*$, then $dA = d(\omega) \otimes (e_\alpha \ot \delta^\beta)$. This is because $d e_\alpha =0, d \delta^\beta=0$ by the definition of local connection $d$ on $E|_U$.
     * 04-08: {{ :math214:note_8_apr_2020.pdf |ipad note}} Connection on Tangent Space. Levi-Cevita connection.
     * 04-10: {{ :math214:note_10_apr_2020_3_.pdf | ipad note}}. Levi-Cevita connection for bi-invariant metric on Lie group. Begin Geodesic equation.
@@ Line 139: / Line 139: @@
     * 04-22: {{ :math214:note_22_apr_2020_2_.pdf |ipad note}}. This follows [Ni]'s lecture note, section 5.2.
     * 04-24:  {{ :math214:note_24_apr_2020_3_.pdf |ipad note}}
+    * [[hw13]]
+  * Week 14: de Rham cohomology
+    * 04-27: {{ :math214:note_27_apr_2020_2_.pdf | ipad note}}
+    * 04-29: {{ :math214:note_29_apr_2020_2_.pdf | note}} Poincare duality. {{ :math214:mv-sequence.pdf |Excerpt from Bott-Tu}}, p23-24, on MV sequence.
+    * 05-01: {{ :math214:note_1_may_2020_2_.pdf | note}}  Singular, Cech, Morse cohomology.
+ ** [[hwsol | Students Homework Solutions]] **
+===== Final =====
+[[final]] and [[final-solution]]

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