# Cup-products in L q,p -cohomology: discretization and quasi-isometry invariance

## TL;DR

This paper establishes a connection between $L^{q,p}$-cohomology of bounded geometry Riemannian manifolds and a metric space notion called packing cohomology, proving its invariance under quasi-isometries and extending results to contact manifolds.

## Contribution

It introduces a new relationship between $L^{q,p}$-cohomology and packing cohomology, demonstrating quasi-isometry invariance and extending to Rumin cohomology on contact manifolds.

## Key findings

- $L^{q,p}$-cohomology is quasi-isometry invariant.
- Established a link between $L^{q,p}$-cohomology and packing cohomology.
- Extended results to Rumin $L^{q,p}$-cohomology on contact manifolds.

## Abstract

We relate $L^{q,p}$-cohomology of bounded geometry Riemannian manifolds to a purely metric space notion of $\ell^{q,p}$-cohomology, packing cohomology. This implies quasi-isometry invariance of $L^{q,p}$-cohomology together with its multiplicative structure. The result partially extends to the Rumin $L^{q,p}$-cohomology of bounded geometry contact manifolds.