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On the anisotropy theorem of Papadakis and Petrotou Xiao, Elizabeth
Abstract
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 Metadata
| Title |
On the anisotropy theorem of Papadakis and Petrotou
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| Creator | |
| Supervisor | |
| Publisher |
University of British Columbia
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| Date Issued |
2023
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| Description |
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.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2023-04-18
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0431106
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Graduation Date |
2023-05
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| Campus | |
| Scholarly Level |
Graduate
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Attribution-NonCommercial-NoDerivatives 4.0 International