On an algorithm for topological data analysis by a variant of Reeb graphs:
and a flashy exposition for commercial use:
A. Zomorodian, Gunnar Carlsson, Computing persistent homology, Discrete Comput. Geom. 33, 249–274 (2005)
Gunnar Carlsson, V. de Silva, Zigzag persistence, arXiv:0812.0197
Gunnar Carlsson, Persistent Homology and Applied Homotopy Theory, in: Handbook of Homotopy Theory, CRC Press, 2019 (arXiv:2004.00738)
Introducing zigzag persistence, connecting persistent homology to quiver representation-theory, re-proving Gabriel's theorem for the case of A-type quivers and introducing the diamond principle:
and applied to level sets:
Gunnar Carlsson, Vin de Silva, Dmitriy Morozov, Zigzag persistent homology and real-valued functions, in: SCG ‘09: Proceedings of the twenty-fifth annual symposium on Computational geometry (2009) 247–256 doi:10.1145/1542362.1542408
Gunnar Carlsson, Vin de Silva, Sara Kališnik, Dmitriy Morozov, Parametrized Homology via Zigzag Persistence, Algebr. Geom. Topol. 19 (2019) 657-700 arXiv:1604.03596, doi:10.2140/agt.2019.19.657
Segal conjecture, Sullivan conjecture
Burnside ring, stable cohomotopy, equivariant stable cohomotopy
Last revised on May 26, 2022 at 15:50:39. See the history of this page for a list of all contributions to it.