Milnor-Wood inequalities for products

TL;DR

This paper proves Milnor-Wood inequalities for local products of manifolds and applies these results to confirm the generalized Chern Conjecture for certain product manifolds involving surfaces.

Contribution

It introduces Milnor-Wood inequalities for local products and verifies the generalized Chern Conjecture for large product manifolds involving surfaces.

Findings

Milnor-Wood inequalities established for local products.

Generalized Chern Conjecture proven for products of manifolds with multiple surfaces.

Results hold for sufficiently large products.

Abstract

We prove Milnor-Wood inequalities for local products of manifolds. As a consequence, we establish the generalized Chern Conjecture for products $M\times \Sigma^k$ for any product of a manifold $M$ with a product of $k$ copies of a surface $\Sigma$ for $k$ sufficiently large.