Updates the readme

README.md

@@ -1,15 +1,44 @@
-My thesis
+Rational Homotopy Theory
-=========
+========================
 
-At the time of writing this repo consists of some notes only.
+Master thesis on Rational Homotopy Theory, the study of homotopy without
-Will be about rational homotopy theory or something.
+torsion. The thesis mainly focuses on the Sullivan equivalence, which models
+rational spaces by commutative differential graded algebras (contrary to
+Quillen's dual approach which considers coalgebras). These objects are nice
+since they are very similar to polynomial rings and hence allow for easy
+calculations. The construction which allows us to go back and forth between
+spaces and algebras resembles ideas from differential geometry (namely De Rham's
+cochain complex), but can be applied to any topological space. Applications
+include the calculation of all rational homotopy groups of all spheres (in
+contrast to the integral case where many groups remain unknown as of today) and
+a result towards Adams' theorem (stating that only the spheres S0, S1, S3 and S7
+are H-spaces).
 
-## building
-It will create a build directory for all those stupid latex files.
 
-```
+## Contents:
-cd thesis
-make
-open thesis.pdf
-```
 
+1. Basics of Rational Homotopy theory
+	- Rational Homotopy Theory
+	- Serre Theorems mod C
+	- Rationalizations
+
+2. CDGAs as Algebraic Models
+	- Homotopy theory for CDGAs
+	- Polynomial Forms
+	- Minimal Models
+	- The Main Equivalence
+
+3. Applications and Further Topics
+	- Rational Homotopy Groups of the Spheres and Other Calculations
+	- Further Topics
+
+4. Appendices
+	- Differential Graded Algebra
+	- Model Categories
+
+
+## Building the pdf
+
+	cd thesis
+	make
+	open thesis.pdf