IMMERSIONS AND EMBEDDINGS OF QUASITORIC MANIFOLDS OVER THE CUBE

{\DJ}or{\dj}e Baralic

Abstract: 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 $N(M^{2n})\geq 8n-3$.

Keywords: quasitoric manifolds, the cube, the Stiefel–Whitney classes, immersions, embeddings

Classification (MSC2000): 57N35, 57R20; 52B20

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