141 citations · 340 across the 18 of their papers we have counts for
24 papers
Approximability for Lagrangian submanifolds
Giovanni Ambrosioni, Paul Biran, Octav Cornea
This paper introduces a notion of categorical approximability for metric spaces that can be viewed as a categorification of approximability for metric groups, as defined by Turing…
Persistence K-theory
Paul Biran, Octav Cornea, Jun Zhang
This paper studies the basic K-theoretic properties of a triangulated persistence category (TPC). This notion was introduced in our earlier papers on triangulation, persistence, an…
Triangulation, Persistence, and Fukaya categories
Paul Biran, Octav Cornea, Jun Zhang
This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a…
Triangulation and persistence: Algebra 101
Paul Biran, Octav Cornea, Jun Zhang
This paper lays the foundations of triangulated persistence categories (TPC), which brings together persistence modules with the theory of triangulated categories. As a result we i…
Bounds on the Lagrangian spectral metric in cotangent bundles
Paul Biran, Octav Cornea
Let be a closed manifold and a bounded domain in the cotangent bundle of , containing the zero-section. A conjecture due to Viterbo asserts that the spect…
A Lagrangian Pictionary
Paul Biran, Octav Cornea
The purpose of this paper is to describe a dictionary geometry <--> algebra in Lagrangian topology. As a by-product we obtain a tautological (in a sense explained in the body of th…