Embeddingof a finite $CW$-complex in a sphere

Ya. N. Shapiro

Leningrad State University named after A. A. Zhdanov

Abstract: The following theorem is proven: for any finite $CW$-complex X of dimensionality n, no one can provide the Euclidean sphere of dimensionality $(n+1)(n+2)/2$ with a $CW$-complex structure such that $X$ will turn out to be isomorphic to some subcomplex of this $CW$-complex.

UDC: 513.83

Received: 29.01.1968

 English version: Mathematical Notes, 1968, 4:6, 891–894

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