Applied and Computational Topology Software

• OAT (Open Applied Topology)

• TTK (Topology Took Kit)

• SeqSee (Spectral Sequence Software)

• GUDHI

• CGAL (Computational Geometry Algorithms Library)

• CHOMP Topology Software (Rutgers)

• Dionysus

• JavaPlex

• Perseus

• PHAT (Persistent Homology Algorithm Toolbox)

• Ripser

Spectral Data Analysis and Manifold Learning Software

• pyDiffMap (Python Diffusion Maps Library)

• jmbr/diffusion-maps (Python Diffusion Maps Library)

• dbMAP (Diffusion-Based Manifold Approximation and Projection)

• Ann Lee's Diffusion Maps Software

• Functional Diffusion Maps

• scikit-learn Manifold Learning (including Laplacian Eigenmaps)

• Laplacian Eigenmaps (multicore)

• Laplacian Eigenmaps and Diffusion Maps in MatLab

• Laplacian Eigenmaps in R

• MatLab Toolbox for Dimensionality Reduction

• Laplacian Eigenmaps Python Implementation

• UMAP Software

• umap-learn (Python)

• UMAP in MatLab

• UMAP in R

• DREiMac (Dimensionality Reduction with Eilenberg-MacLane Coordinates)

Fast Approximate Nearest-Neighbor Software Libraries

• flann (Fast Library for Approximate Nearest-Neighbors)

• nmslib (Non-Metric-Space Library - similarity search)

Mathematics Blogs/Wiki-Style Resources

• Applied Topology Blog

• Combinatorics and More (Gil Kalai's blog)

• Gowers's Weblog (Timothy Gowers' blog)

• Mathematical Field Notes (Johnny Evans' blog)

• n-Category Café

• Symplectic Field Theorist (Chris Wendl's blog)

• What's New (Terrence Tao's blog) 

• Stacks Project

University Applied Topology Research Groups

• (CIMAT Guanajuato) Applied Geometry and Topology Group

• (CMU) Topological Statistics Group

• (EPFL) Applied Topology Seminar

• (INRIA) Datashape Group (formerly Geometrica)

• (LBNL) Data Analysis and Visualization Group

• (Michigan State) Computational Mathematics, Science, and Engineering Department

• (Queen Mary) Applied Algebraic Topology Seminar (archive)

• (Stanford) Applied Topology Blog

Applied Topology Research Networks

• Applied Algebraic Topology Research Network

• CHomP (Computational Homology Project)

• UK Centre for Topological Data Analysis

• TOPDRIM (EU Project) (no longer active)

Journals