Studying the first non-vanishing cohomology group of the Orlik-Solomon algebra for triangle-free graph related graphic arrangements
Abstract
In this work, we examine the vanishing of the second cohomology group of the Orlik- Solomon algebra , denoted by , corresponding to the graphic arrangement related with a triangle-free graph . Here, specifies the number of edges in and is defined as , for . Motivated by this goal, we investigate as a free module and show that it does not vanish when contains chordless 4-cycles including the edges and .
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References
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