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Elliptic Cohomology

There is a (class of) generalized cohomology theory called the elliptic cohomology theory. As the name suggest, it is defined by the formal group law associated to an elliptic curve . It was made public by the proceedings [ Ell88 ] . This book is still a good starting point. For a modern treatment, see Lurie’s exposition .

The elliptic cohomology theory is supposed be the “cohomology theory next to K -theory ” in various senses.

In homotopy theory, one of the most popular variants of elliptic cohomology theory is the topological modular forms spectrum tmf . Experimental calculations with tmf have been performed. Hill computed the 3-local tmf homology of B Σ 3 in [ Hil ] .

References