Every finite d-dimensional simplicial complex is a deformation retract of a (2d-1)-dimensional pseudomanifold with boundary and embeds as a retract in a closed (2d-1)-dimensional pseudomanifold.
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Embedding complexes into pseudomanifolds
Every finite d-dimensional simplicial complex is a deformation retract of a (2d-1)-dimensional pseudomanifold with boundary and embeds as a retract in a closed (2d-1)-dimensional pseudomanifold.