| In this dissertation we construct an explicit representative for the Grothendieck fundamental class [Z] ∈ Ext r( OZ,Wr X ) of a complex submanifold Z of a complex manifold X such that Z is the zero locus of a real analytic section of a holomorphic vector bundle E of rank r on X. To this data we associate a super-connection A on &bigand;* E∨ , which gives a "twisted resolution" T* of OZ such that the "generalized super-trace" of 1r! A2r, which is a map of complexes from T* to the Dolbeault complex Ar,*X , represents [Z]. One may then read off the Gauss-Bonnet formula from this map of complexes. |
