Fixes a typo and adds a todo

thesis/notes/Basics.tex

@@ -78,7 +78,7 @@ The following two theorems can be found in textbooks about homological algebra s
 The latter two theorems have a direct consequence for rational homotopy theory. By taking $A = \Q$ we see that the torsion groups vanish. We have the immediate corollary.
 
 \Corollary{rational-corollaries}{
-	We have the following natural isomorphisms in rational homology, and we can relate rational cohomolgy naturally to rational homology
+	We have the following natural isomorphisms in rational homology, and we can relate rational cohomology naturally to rational homology
 	\begin{align*}
 		H_\ast(X) \tensor \Q &\tot{\iso} H_\ast(X; \Q), \\
 		H_\ast(X; \Q) \tensor H_\ast(Y; \Q) &\tot{\iso} H_\ast(X \times Y; \Q), \\

thesis/notes/Homotopy_Groups_CDGA.tex

@@ -36,3 +36,5 @@ Consider the augmented cdga $V(n) = S(n) \oplus \k$, with trivial multiplication
 }
 
 From now on the dual of a vector space will be denoted as $V^\ast = \Hom_\k(V, \k)$. So the above lemma states that there is a bijection $[A, V(n)] \iso \pi^n(A)^\ast$.
+
+\todo{long exact sequence}