New bounds on the toral rank with application to cohomologically symplectic spaces
arXiv:1711.02901
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 .
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