Integral foliated simplicial volume and ergodic decomposition
Clara Loeh, Giovanni Sartori
TL;DR
This paper introduces an integration formula for integral foliated simplicial volume using ergodic decompositions, drawing an analogy to the ergodic decomposition formula for group cost, thereby advancing the understanding of these invariants.
Contribution
It provides a new integration formula for integral foliated simplicial volume based on ergodic decompositions, connecting geometric invariants with ergodic theory.
Findings
Established an ergodic decomposition formula for integral foliated simplicial volume.
Connected the concept with the ergodic decomposition formula for group cost.
Enhanced the theoretical framework linking geometric invariants and ergodic theory.
Abstract
We establish an integration formula for integral foliated simplicial volume along ergodic decompositions. This is analogous to the ergodic decomposition formula for the cost of groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric Analysis and Curvature Flows · Geometry and complex manifolds