Extending the group

The library natively supports all groups \(G=C_{2^n}\) but can easily be extended to \(G=C_{p^n}\) for prime \(p\).
The input remaining is \(C_*(S^V)\) for \(V\) a non-virtual \(G\)-rep. See C2n.hpp or C4.hpp for examples.

Note: The algorithm used in C2n.hpp is based on the recursion established in HHR17 pg 392

Todo:: Implement all \(G=C_{p^n}\)

For general cyclic groups the subgroup diagram is not a vertical tower so the transfer and restriction algorithms will need reworking to take that into account

Todo:: Support arbitrary cyclic groups by using a subgroup diagram-tree for transfers and restrictions

For more general finite abelian groups we would also need to specify the order of the elements of the group and how they relate to the subgroup diagram to form our equivariant bases.

Todo:: Support general finite abelian groups

Extending the coefficients

The library natively supports \(\mathbf Z\) and \(\mathbf Z/p\) constant coefficients. See Z_n.hpp for the implementation of the latter.

For non constant coefficients transferring becomes much more complicated as the modules involved in the free Mackey functors are no longer of the form \(\oplus_HR[G/H]\).

Todo:: Support non constant coefficients such as Burnside ring coefficients \(A_{\mathbf Z}\)

Table of Contents

Extending the group

Extending the coefficients