# Domination between different products and finiteness of associated semi-norms

## TL;DR

This paper characterizes domination relations between products of manifolds and establishes the finiteness of associated semi-norms, providing partial answers to Gromov's questions on manifold invariants.

## Contribution

It determines all possible dominations between product manifolds with certain restrictions and proves the finiteness of related semi-norms on their fundamental classes.

## Key findings

- All domination relations between specified product manifolds are classified.
- Finiteness of product-associated semi-norms on fundamental classes is established.
- Results partially answer questions posed by M. Gromov.

## Abstract

In this note we determine all possible dominations between different products of manifolds, when none of the factors of the codomain is dominated by products. As a consequence, we determine the finiteness of every product-associated functorial semi-norm on the fundamental classes of the aforementioned products. These results give partial answers to questions of M. Gromov.