An Intersection Product for the Polytope Algebra
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912367116288000 |
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| author | Wannerer, Thomas |
| author_facet | Wannerer, Thomas |
| contents | We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise naturally from this construction. These subalgebras can be regarded as volumetric analogues of the graded Möbius algebra, which appears in the context of the Dowling-Wilson conjecture. We conjecture that they also satisfy the injective hard Lefschetz property and the Hodge-Riemann relations, and we prove these in degree one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Intersection Product for the Polytope Algebra Wannerer, Thomas Combinatorics Metric Geometry We introduce a new multiplication for the polytope algebra, defined via the intersection of polytopes. After establishing the foundational properties of this intersection product, we investigate finite-dimensional subalgebras that arise naturally from this construction. These subalgebras can be regarded as volumetric analogues of the graded Möbius algebra, which appears in the context of the Dowling-Wilson conjecture. We conjecture that they also satisfy the injective hard Lefschetz property and the Hodge-Riemann relations, and we prove these in degree one. |
| title | An Intersection Product for the Polytope Algebra |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2504.16678 |