# Alternate proofs for the $n$-dimensional resolution theorems

## TL;DR

This paper introduces simplified, unified proofs for key resolution theorems in topology, using innovative techniques to convert cohomology problems into homology problems and providing a general method for constructing necessary maps.

## Contribution

It offers new, streamlined proofs for resolution theorems, enhancing understanding and applicability in algebraic topology.

## Key findings

- Simplified proofs for cell-like, $ ext{Z}/p$, and $ ext{Q}$-resolution theorems.
- A general topological method for constructing resolution maps.
- Conversion of cohomology problems into homology problems.

## Abstract

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups. We provide a coordinated general topological method for constructing the maps needed to witness the resolution theorems simultaneously.