141 citations · 340 across the 18 of their papers we have counts for
19 papers · 1 filter
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…
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…
Lagrangian Shadows and Triangulated Categories
Paul Biran, Octav Cornea, Egor Shelukhin
Under certain assumptions (such as weak exacteness or monotonicity) we show that splitting Lagrangians through cobordism has an energy cost and, from this cost being smaller than c…