A quasitoric manifold $M^{2n}$ over the cube $I^n$ is studied. The Stiefel–Whitney classes are calculated and used as the obstructions for immersions, embeddings and totally skew embeddings. The manifold $M^{2n}$, when $n$ is a power of 2, has interesting properties: $operatorname{imm}(M^{2n})=4n-2$, $operatorname{em}(M^{2n})=4n-1$ and $N(M^{2n})geq 8n-3$.
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机译：研究了在立方体$ I ^ n $上的准流形$ M ^ {2n} $。计算Stiefel–Whitney类，并将其用作沉浸，嵌入和完全偏斜嵌入的障碍。流元$ M ^ {2n} $，当$ n $是2的幂时，具有有趣的属性：$ operatorname {imm}（M ^ {2n}）= 4n-2 $，$ operatorname {em}（ M ^ {2n}）= 4n-1 $和$ N（M ^ {2n}） geq 8n-3 $。
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