| Tools for concrete calculations include algebraic K-theory and motivic cohomology. |
| Two objects that can be deformed into one another will have the same homology and cohomology groups. |
| At her instigation a number of people then produced a theory of these groups, the so-called homology and cohomology groups of a space. |
| Deligne used a new theory of cohomology called étale cohomology, drawing on ideas originally developed by Alexandre Grothendieck some 15 years earlier, and applied them to solve the deepest of the Weil conjectures. |
| We will first study equivariant cohomology on some examples. |
| In further papers, published in 1936, he defined cohomology groups for an arbitrary locally compact topological space. |
