On the f-invariant of products

TL;DR

This paper computes the f-invariant for products of framed manifolds, extending the understanding of higher invariants in topology by relating it to e-invariants of the factors.

Contribution

It provides a complete determination of the f-invariant for products of framed manifolds, linking it explicitly to the e-invariants of the individual factors.

Findings

f-invariant of product manifolds can be computed from e-invariants

Provides explicit formulas for the f-invariant in product cases

Enhances understanding of higher invariants in topology

Abstract

The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; in the situation of a cartesian product of two framed manifolds, the f-invariant can actually be computed from the e-invariants of the factors. The purpose of this note is to determine the f-invariant of all such products.