Difference between revisions of "Topology"

From Ioannis Kourouklides
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==Books==
 
==Books==
 
* Boissonnat, J. D., Chazal, F., & Yvinec, M. (2018). ''Geometric and Topological Inference''. Cambridge University Press. ([https://geometrica.saclay.inria.fr/team/Fred.Chazal/papers/CGLcourseNotes/main.pdf link])
 
* Boissonnat, J. D., Chazal, F., & Yvinec, M. (2018). ''Geometric and Topological Inference''. Cambridge University Press. ([https://geometrica.saclay.inria.fr/team/Fred.Chazal/papers/CGLcourseNotes/main.pdf link])
* Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., ... & Ziegelmeier, L. (2017). Persistence images: A stable vector representation of persistent homology. ''The Journal of Machine Learning Research, 18''(1), 218-252.
 
 
* Oudot, S. Y. (2015). ''Persistence Theory: From Quiver Representations to Data Analysis ''. American Mathematical Society.
 
* Oudot, S. Y. (2015). ''Persistence Theory: From Quiver Representations to Data Analysis ''. American Mathematical Society.
  

Revision as of 18:49, 25 December 2018

This page contains resources about Geometric Topology and Topology in general.

Subfields and Concepts

  • Metric Geometry 
    • Metric / Distance function
    • Geodesics
  • Topological Groups
    • Pontryagin duality (in Harmonic Analysis)
    • Locally Compact Abelian Group (LCA Group or LCAG)
  • Topological Spaces
    • Manifold
      • Riemannian Manifolds
    • Metric space
      • Riemannian metric
      • Fisher information metric / Fisher–Rao metric
  • Topological Data Analysis
    • barcode / persistence diagram
    • persistent homology / topological persistence

Online Courses

Video Lectures

Lecture Notes

Books

  • Boissonnat, J. D., Chazal, F., & Yvinec, M. (2018). Geometric and Topological Inference. Cambridge University Press. (link)
  • Oudot, S. Y. (2015). Persistence Theory: From Quiver Representations to Data Analysis . American Mathematical Society.

Scholarly Articles

  • Bubenik, P. (2015). Statistical topological data analysis using persistence landscapes. The Journal of Machine Learning Research, 16(1), 77-102.

Software

See also

Other Resources