Four lectures on scalar curvature
M Gromov - arXiv preprint arXiv:1908.10612, 2019 - arxiv.org
arXiv:1908.10612v6 [math.DG] 8 Jul 2021 Page 1 arXiv:1908.10612v6 [math.DG] 8 Jul 2021
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
Four Lectures on Scalar Curvature Misha Gromov July 9, 2021 Unlike manifolds with controlled …
[图书][B] Topological persistence in geometry and analysis
The theory of persistence modules originated in topological data analysis and became an
active area of research in algebraic topology. This book provides a concise and self …
active area of research in algebraic topology. This book provides a concise and self …
Viterbo conjecture for Zoll symmetric spaces
E Shelukhin - Inventiones mathematicae, 2022 - Springer
We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the
Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent …
Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent …
Bounds on spectral norms and barcodes
A Kislev, E Shelukhin - Geometry & Topology, 2022 - msp.org
We investigate the relations between algebraic structures, spectral invariants and
persistence modules, in the context of monotone Lagrangian Floer homology with …
persistence modules, in the context of monotone Lagrangian Floer homology with …
Persistent homology and applied homotopy theory
G Carlsson - Handbook of Homotopy Theory, 2020 - taylorfrancis.com
The output of standard persistent homology is represented in two ways, via persistence
barcodes and persistence diagrams. Initially persistent homology was used, as homology is …
barcodes and persistence diagrams. Initially persistent homology was used, as homology is …
Hamiltonian pseudo-rotations of projective spaces
VL Ginzburg, BZ Gürel - Inventiones mathematicae, 2018 - Springer
The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of CP^ n CP n
with the minimal possible number of periodic points (equal to n+ 1 n+ 1 by Arnold's …
with the minimal possible number of periodic points (equal to n+ 1 n+ 1 by Arnold's …
Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective
E Cineli, VL Ginzburg, BZ Gurel - arXiv preprint arXiv:2111.03983, 2021 - arxiv.org
We study topological entropy of compactly supported Hamiltonian diffeomorphisms from a
perspective of persistence homology and Floer theory. We introduce barcode entropy, a …
perspective of persistence homology and Floer theory. We introduce barcode entropy, a …
Proof of the simplicity conjecture
D Cristofaro-Gardiner, V Humilière… - arXiv preprint arXiv …, 2020 - arxiv.org
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving
homeomorphisms of the $ n $-ball is simple for $ n\ge 3$, asked if the same statement holds …
homeomorphisms of the $ n $-ball is simple for $ n\ge 3$, asked if the same statement holds …
Barcodes and area-preserving homeomorphisms
F Le Roux, S Seyfaddini, C Viterbo - Geometry & Topology, 2021 - msp.org
We use the theory of barcodes as a new tool for studying dynamics of area-preserving
homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of a …
homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of a …
On the growth of the Floer barcode
E Cineli, VL Ginzburg, BZ Gurel - arXiv preprint arXiv:2207.03613, 2022 - arxiv.org
This paper is a follow up to the authors' recent work on barcode entropy. We study the
growth of the barcode of the Floer complex for the iterates of a compactly supported …
growth of the barcode of the Floer complex for the iterates of a compactly supported …