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ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS

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Title
ENTROPY OF THE COMPOSITION OF TWO SPHERICAL TWISTS
Author(s)
Barbacovi, Federico; Jongmyeong Kim
Publication Date
2023-07
Journal
Osaka Journal of Mathematics, v.60, no.3, pp.653 - 670
Publisher
Osaka University
Abstract
Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of two endofunctors is hard, and in general the result doesn’t have to be related to the entropy of the single pieces. In this paper we compute the entropy of the composition of two spherical twists around spherical objects, showing that it depends on the dimension of the graded vector space of morphisms between them. As a consequence of these computations we produce new counterexamples to Kikuta–Takahashi’s conjecture. In particular, we describe the first counterexamples in odd dimension and examples for the d-Calabi–Yau Ginzburg dg algebra associated to the A2 quiver. © 2022, All rights reserved.
URI
https://pr.ibs.re.kr/handle/8788114/14492
ISSN
0030-6126
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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