

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 3local
tmf
homology of
B
Σ
_{
3
}
in
[
Hil
]
.


