The Schönflies conjecture

Sammanfattning

In this degree project we define elementary notions of differential topology aswell as n-dimensional k-handles and relate these to Morse theory. Moreover, we define integral Morse homology and reference its equivalence to singularhomology. We then go on to state the Schönflies conjecture and prove it forn > 5 by induction over the Morse chain complex using handle slides and the Whitney trick. Having completed the proof, we relate the Schönflies conjectureto the h-cobordism theorem and the generalised Poincar´e conjecture.