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Computational Topology - an Introduction

- H. Edelsbrunner, J. Harer
- Computer Science
- 8 December 2009

TLDR

Stability of persistence diagrams

- D. Cohen-Steiner, H. Edelsbrunner, J. Harer
- MathematicsSCG
- 6 June 2005

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram… Expand

Persistent Homology — a Survey

- H. Edelsbrunner, J. Harer
- Mathematics

Persistent homology is an algebraic tool for measuring topological features of shapes and functions. It casts the multi-scale organization we frequently observe in nature into a mathematical… Expand

Combinatorics of Train Tracks.

Measured geodesic laminations are a natural generalization of simple closed curves in surfaces, and they play a decisive role in various developments in two-and three-dimensional topology, geometry… Expand

Stability of the homology of the mapping class groups of orientable surfaces

- J. Harer
- Mathematics
- 1 March 1985

The mapping class group of F = Fgs r is F = rgs = wo(A) where A is the topological group of orientation preserving diffeomorphisms of F which are the identity on dF and fix the s punctures. When r =… Expand

The virtual cohomological dimension of the mapping class group of an orientable surface

- J. Harer
- Mathematics
- 1 February 1986

Let F = F ~ r be the mapping class group of a surface F of genus g with s punctures and r boundary components. The purpose of this paper is to establish cohomology properties of F parallel to those… Expand

The second homology group of the mapping class group of an orientable surface

- J. Harer
- Mathematics
- 1 June 1983

In I-7] Mumford shows that the Picard group P ic (~ ' ) is isomorphic to H2(F; 2~) and conjectures the latter is rank one, g>3 . We prove this below for g>5 . Another interpretation of this theorem… Expand

Stability of Persistence Diagrams

- D. Cohen-Steiner, H. Edelsbrunner, J. Harer
- MathematicsDiscret. Comput. Geom.
- 2007

The persistence diagram of a real-valued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram… Expand

Hierarchical morse complexes for piecewise linear 2-manifolds

- H. Edelsbrunner, J. Harer, A. Zomorodian
- MathematicsSCG '01
- 1 June 2001

TLDR

Hierarchical Morse—Smale Complexes for Piecewise Linear 2-Manifolds

- H. Edelsbrunner, J. Harer, A. Zomorodian
- MathematicsDiscret. Comput. Geom.
- 21 May 2003

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