The homology and cohomology of the complements to some arrangements of codimension two complex planes

Yu. V. Èliyashev

Siberian Federal University, Krasnoyarsk

Abstract: We consider the homology and cohomology of the complement to the arrangement $Z=\bigcup_{1<|i-j|<d-1}\{z_i=z_j=0\}$ of coordinate planes in $\mathbb C^d$, and explicitly construct a basis for these groups as well as a basis for the homology groups of the one-point compactification of $Z$.

Keywords: plane arrangement, homology, cohomology, complement, one-point compactification.

UDC: 515.16+517.55

Received: 22.09.2009

 English version: Siberian Mathematical Journal, 2011, 52:3, 554–562

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