The Charney-Davis conjecture for certain subdivisions of spheres
Andrew Frohmader
TL;DR
This paper introduces sesquiconstructible complexes and odd iterated stellar subdivisions, then proves the Charney-Davis conjecture for these subdivisions of sesquiconstructible spheres and balls.
Contribution
It establishes the Charney-Davis conjecture for a new class of subdivisions, expanding the conjecture's verified cases.
Findings
Sesquiconstructible complexes are characterized and their properties verified.
The Charney-Davis conjecture is proven for odd iterated stellar subdivisions of these complexes.
New classes of complexes satisfying the conjecture are identified.
Abstract
Notions of sesquiconstructible complexes and odd iterated stellar subdivisions are introduced, and some of their basic properties are verified. The Charney-Davis conjecture is then proven for odd iterated stellar subdivisions of sesquiconstructible balls and spheres.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory