Modular invariance and anomaly cancellation formulas in odd dimension

TL;DR

This paper investigates modular invariance of characteristic forms to derive new anomaly cancellation formulas in odd-dimensional manifolds, leading to results on index divisibility and characteristic number congruences.

Contribution

It introduces novel anomaly cancellation formulas in odd dimensions based on modular invariance, expanding understanding of characteristic forms and index theory.

Findings

New anomaly cancellation formulas in (4r-1)-dimensional manifolds.

Divisibility results for the index of Toeplitz operators.

Congruence formulas for characteristic numbers on spin^c manifolds.

Abstract

By studying modular invariance properties of some characteristic forms, we get some new anomaly cancellation formulas on $(4r-1)$ dimensional manifolds. As an application, we derive some results on divisibilities of the index of Toeplitz operators on $(4r-1)$ dimensional spin manifolds and some congruent formulas on characteristic number for $(4r-1)$ dimensional spin$^c$ manifolds.