New bounds on the toral rank with application to cohomologically symplectic spaces

2017/11/08 by Leopold Zoller, Zoller, Leopold
Mathematics · #13D02 #55N91 #57S25 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:13D02 #msc:55N91 #msc:57S25

paper · pdf · doi:10.48550/arxiv.1711.02901

It was pointed out to the author that our proofs of Thm A and to a certain extent also Thm B already appear in the literature. While most of versions 1 and 2 coincide, we have adjusted the introduction and section 2 by removing the proof of what was Thm A and properly referencing the original sources

arxiv created 2018/01/14 · arxiv updated 2018/01/16

Abstract

We use Boij-Söderberg theory to give two lower bounds for the dimension of the cohomology of a finite CW-complex in terms of the toral rank and certain Betti numbers of the space. One of our bounds turns out to be particularly effective for c-symplectic spaces, proving the toral rank conjecture for c-symplectic spaces of formal dimension ≤ 8.

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