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Calabi-Yau Three-folds: Poincare Polynomials and Fractals

Ashmore, A. & He, Y. (2011). Calabi-Yau Three-folds: Poincare Polynomials and Fractals. In: Strings, Gauge Fields, and the Geometry Behind: The Legacy of Maximilian Kreuzer. (pp. 173-186). World Scientific Publishing Company. doi: 10.1142/9789814412551_0007


We study the Poincar´e polynomials of all known Calabi-Yau three-folds as constrained polynomials of Littlewood type, thus generalising the wellknown investigation into the distribution of the Euler characteristic and Hodge numbers. We find interesting fractal behaviour in the roots of these polynomials in relation to the existence of isometries, distribution versus typicality, and mirror symmetry.

Publication Type: Book Section
Additional Information: Calabi-Yau Three-folds: Poincare Polynomials and Fractals, YANG-HUI HE, Copyright 2011 with permission from World Scientific Publishing Co. Pte. Ltd.
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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