E. Kogan

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math.GT2026

Embeddings of $k$ -complexes in $2 k$ -manifolds and minimum rank of partial symmetric matrices

A. Skopenkov

Let $K$ be a $k$ -dimensional simplicial complex having $n$ faces of dimension $k$ , and $M$ a closed $(k - 1)$ -connected PL $2 k$ -dimensional manifold. We prove that for $k \geq 3$ odd $K…

math.GT2026

A short proof of the Patak-Tancer theorem on non-embeddability of $k$ -complexes in $2 k$ -manifolds

E. Kogan, A. Skopenkov

In 2019 P. Patak and M. Tancer obtained the following higher-dimensional generalization of the Heawood inequality on embeddings of graphs into surfaces. We present a short well-str…

Embeddings of k-complexes in 2k-manifolds and minimum rank of partial symmetric matrices

A short proof of the Patak-Tancer theorem on non-embeddability of k-complexes in 2k-manifolds

Embeddings of $k$ -complexes in $2 k$ -manifolds and minimum rank of partial symmetric matrices

A short proof of the Patak-Tancer theorem on non-embeddability of $k$ -complexes in $2 k$ -manifolds