Algebraic Topology of Calabi-Yau Threefolds in Toric Varieties
  We compute the integral homology (including torsion), the topological K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold hypersurfaces and complete intersections in Gorenstein toric Fano varieties. The methods are purely topological. 
Charles F. Doran and John W. Morgan