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A NOTE ON ENTROPY OF AUTO-EQUIVALENCES: LOWER BOUND AND THE CASE OF ORBIFOLD PROJECTIVE LINES

Part of: Topological dynamics Abelian categories (Co)homology theory Homological methods

Published online by Cambridge University Press:  26 June 2018

KOHEI KIKUTA ,
YUUKI SHIRAISHI  and
ATSUSHI TAKAHASHI
KOHEI KIKUTA
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan email k-kikuta@cr.math.sci.osaka-u.ac.jp
YUUKI SHIRAISHI
Affiliation:
International college, Osaka University, Toyonaka, Osaka, 560-0043, Japan email shiraishi@cbcmp.icou.osaka-u.ac.jp
ATSUSHI TAKAHASHI
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan email takahashi@math.sci.osaka-u.ac.jp
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Abstract

Entropy of categorical dynamics is defined by Dimitrov–Haiden–Katzarkov–Kontsevich. Motivated by the fundamental theorem of the topological entropy due to Gromov–Yomdin, it is natural to ask an equality between the entropy and the spectral radius of induced morphisms on the numerical Grothendieck group. In this paper, we add two results on this equality: the lower bound in a general setting and the equality for orbifold projective lines.

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions 16E35: Derived categories 18E30: Derived categories, triangulated categories 37B40: Topological entropy
Type
Article
Information
Nagoya Mathematical Journal , Volume 238 , June 2020 , pp. 86 - 103
Copyright
© 2018 Foundation Nagoya Mathematical Journal

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