On the automorphism group of Danielewski surfaces

Abstract: In this thesis we define the notion of an overshear on a Danielewski surface. We show that the group generated by the overshears is dense (in the compact open topology) in the automorphism group for small degrees of the defining polynomial. It is also shown in the thesis that the overshear group has a structure of an amalgamated product. Finally, we show that the Danielewski surfaces have the Oka-Grauert property.