Connective topological modular form has led to a lot of important calculations in chromatic homotopy theory. One of the key features of is that its cohomology as a module over Steenrod algebra is isomorphic to , where is a subalgebra of A generated by . On the other hand, is an exterior element of . For any A-module one can define a chain complex where the action of acts as a differential and its homology is the Margolis homology . The calculation Margolis homology is not straightforward as the action do not follow Leibniz rule. In this talk, we will develope a new technique that will allow us to calculate Margolis homology. In particular we will give a complete answer for Margolis homology of .
The P_2^1 Margolis homology of the connective topological modular form.