chapter
1 Pages

Introduction to Part III

WithMarvin J. Greenberg, John R. Harper

Manifolds are the main geometric topic of part III. A new theoretical tool, cohomology, is introduced. Cup and cap products are introduced by means of the Alexander-Whitney map. The cup product endows cohomology with more algebraic structure than was available for homology in chapter 19. The cap product from cohomology to homology is used for the duality theorems.