Embedding complexes into pseudomanifolds

TL;DR

The paper demonstrates that any finite d-dimensional simplicial complex can be embedded as a deformation retract into a higher-dimensional pseudomanifold, providing a new way to realize complexes within pseudomanifolds.

Contribution

It introduces a method to embed and retract finite simplicial complexes into higher-dimensional pseudomanifolds, expanding understanding of their topological embeddings.

Findings

Any finite d-dimensional simplicial complex is a deformation retract of a (2d-1)-dimensional pseudomanifold.

Such complexes can be embedded as a retract in a closed (2d-1)-dimensional pseudomanifold.

The results hold for all d ≥ 2.

Abstract

We show that for $d\geq 2$ every finite $d$-dimensional simplicial complex is a deformation retract of a $(2d-1)$-dimensional pseudomanifold with boundary. Moreover, it embeds as a retract in a closed $(2d-1)$-dimensional pseudomanifold.