A note on modular forms and generalized anomaly cancellation formulas 2

TL;DR

This paper extends generalized anomaly cancellation formulas to even-dimensional manifolds and explores their modularity properties on odd-dimensional manifolds, contributing to the mathematical understanding of characteristic forms and modularity.

Contribution

It introduces new (a, b) type cancellation formulas for even-dimensional manifolds and derives modular characteristic forms for odd-dimensional manifolds.

Findings

New (a, b) cancellation formulas for even-dimensional manifolds

Characteristic forms with modularity properties on odd-dimensional manifolds

Enhanced understanding of anomaly cancellation in geometric contexts

Abstract

In [7], Liu and Wang generalized the Han-Liu-Zhang cancellation formulas to the (a, b) type cancellation formulas. In this note, we prove some another (a, b) type cancellation formulas for even-dimensional Riemannian manifolds. And by transgression, we obtain some characteristic forms with modularity properties on odd-dimensional manifolds.