Mass-growth of triangulated auto-equivalences
Jon Woolf
TL;DR
This paper explores how the mass growth of auto-equivalences in triangulated categories relates to their dynamical actions on stability spaces, revealing conditions for free and proper actions based on mass growth.
Contribution
It establishes a connection between mass growth and the dynamical properties of auto-equivalences on stability condition spaces, providing new insights into their behavior.
Findings
Mass growth correlates with the dynamical behavior of auto-equivalences.
Non-vanishing mass growth implies the action is free and proper.
The work links categorical auto-equivalence properties to geometric dynamics.
Abstract
We relate the mass growth (with respect to a stability condition) of an exact auto-equivalence of a triangulated category to the dynamical behaviour of its action on the space of stability conditions. One consequence is that this action is free and proper whenever the mass growth is non-vanishing.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra