Bott periodicity and stable quantum classes

TL;DR

This paper explores the use of Bott periodicity to connect quantum classes with exotic Chern classes, offering a new framework for computing Gromov-Witten invariants and studying Hamiltonian rigidity in symplectic geometry.

Contribution

It introduces a novel theoretical framework linking quantum classes and exotic Chern classes via Bott periodicity, with applications to Gromov-Witten invariants and Hofer geometry.

Findings

Relation between quantum classes and exotic Chern classes established

Framework for computing Gromov-Witten invariants developed

Insights into Hamiltonian rigidity of complex projective spaces

Abstract

We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on $BU$. This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with cohomological field theories. This framework has applications to study of higher dimensional, Hamiltonian rigidity aspects of Hofer geometry of $ \mathbb{CP} ^{n}$, one of which we discuss here.