Master thesis presentation by Albin Sigurdson

Title: Explorations in the Index Theory of Contact Manifolds

Abstract: The index of the differential operator P=X₂²+X₃²+ \gamma X₁ on the Heisenberg group and the 3-sphere is examined. By results in $K$-homology, the index depends only on the winding numbers of \gamma around odd integers. Both the topological and analytical indices are discussed, with explicit calculations of the former provided. The operator P is described in bases of L²(S³,\C²) and L²(\Gamma\H₃), which in turn are obtained through harmonic analysis and representation theory.

Supervisor: Magnus Goffeng

Examiner: Sigmundur Gudmundsson