UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

On the anisotropy theorem of Papadakis and Petrotou Xiao, Elizabeth


We study the anisotropy theorem for Stanley-Reisner rings of simplicial homology spheres in characteristic 2 by Papadakis and Petrotou. This theorem implies the Hard Lefschetz theorem as well as McMullen's g-conjecture for such spheres. Our first result is an explicit description of the quadratic form. We use this description to prove a conjecture stated by Papadakis and Petrotou. All anisotropy theorems for homology spheres and pseudo-manifolds in characteristic 2 follow from this conjecture. Using a specialization argument, we prove anisotropy for certain homology spheres over the field Q. These results provide another self-contained proof of the g-conjecture for homology spheres in characteristic 2.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International