# Two short proofs of the topological invariance of intersection homology

## TL;DR

This paper presents two concise proofs demonstrating the topological invariance of intersection homology, one relying on specific axioms and the other offering a more adaptable approach for various perversities.

## Contribution

It introduces two novel, succinct proofs of the topological invariance of intersection homology, expanding applicability beyond previous methods.

## Key findings

- One proof is very short but depends on support and cosupport axioms.
- The other proof is longer but more flexible, not requiring these axioms.
- Both proofs establish the topological invariance of intersection homology.

## Abstract

We indicate two short proofs of the Goresky-MacPherson topological invariance of intersection homology. One proof is very short but requires the Goresky-MacPherson support and cosupport axioms; the other is slightly longer but does not require these axioms and so is adaptable to more general perversities.