The connective Morava K-theory of the second mod p Eilenberg-MacLane space

TL;DR

This paper develops computational tools for connective Morava K-theory of spaces, demonstrating their effectiveness by calculating the theory for the second mod p Eilenberg-MacLane space.

Contribution

It introduces a Universal Coefficient Theorem linking cohomology and homology in connective Morava K-theory, enabling explicit calculations.

Findings

Universal Coefficient Theorem established for connective Morava K-theory

Computed the theory for the second mod p Eilenberg-MacLane space

Tools facilitate future computations in the field

Abstract

We develop tools for computing the connective n-th Morava K-theory of spaces. Starting with a Universal Coefficient Theorem that computes the cohomology version from the homology version, we show that every step in the process of computing one is mirrored in the other and that this can be used to make computations. As our example, we compute the connective n-th Morava K-theory of the second mod p Eilenberg-MacLane space.