Weighted circle actions on the Heegaard quantum sphere

TL;DR

This paper studies weighted circle actions on the quantum Heegaard 3-sphere, classifying fixed point algebras and analyzing their algebraic and topological properties, including K-theory and line bundle non-triviality.

Contribution

It introduces quantum weighted Heegaard spheres as fixed point algebras, interprets their coordinate algebras as generalized Weyl algebras, and computes their K-groups and Chern numbers.

Findings

Classification of fixed point algebras as quantum weighted Heegaard spheres

Construction of quantum principal circle bundles and Fredholm modules

Explicit calculation showing non-triviality of associated line bundles

Abstract

Weighted circle actions on the quantum Heeqaard 3-sphere are considered. The fixed point algebras, termed quantum weighted Heegaard spheres, and their representations are classified and described on algebraic and topological levels. On the algebraic side, coordinate algebras of quantum weighted Heegaard spheres are interpreted as generalised Weyl algebras, quantum principal circle bundles and Fredholm modules over them are constructed, and the associated line bundles are shown to be non-trivial by an explicit calculation of their Chern numbers. On the topological side, the C*-algebras of continuous functions on quantum weighted Heegaard spheres are described and their K-groups are calculated.