A Small Polyhedral Z-Acyclic 2-Complex in R4

We present a small 4-dimensional polyhedral realization of a 2-dimensional Z-acyclic but non-contractible simplicial complex.

Authors: Frank H. Lutz, G"unter M. Ziegler

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

Original Paper

Loading high-quality paper...

Comments & Academic Discussion

Loading comments...

Leave a Comment