Non-torsion non-algebraic classes in the Brown-Peterson tower

TL;DR

This paper constructs non-torsion non-algebraic elements in the Brown-Peterson tower at prime 2, extending previous work on torsion classes and classical results on non-algebraic classes.

Contribution

It introduces the first known examples of non-torsion non-algebraic classes in the Brown-Peterson tower for prime 2.

Findings

Constructed non-torsion non-algebraic elements in the Brown-Peterson tower at prime 2.

Extended the understanding of non-algebraic classes beyond torsion cases.

Generalized classical results of Atiyah and Hirzebruch.

Abstract

Generalizing the classical work of Atiyah and Hirzebruch on non-algebraic classes, recently Quick proved the existence of torsion non-algebraic elements in the Brown-Peterson tower. We construct non-torsion non-algebraic elements in the Brown-Peterson tower for the prime number 2.