More Like this

1. Heegaard Floer homology and splicing homology spheres

   https://doi.org/10.4310/MRL.2021.v28.n1.a4  

   Karakurt, Çağrı; Lidman, Tye; Tweedy, Eamonn (January 2021, Mathematical Research Letters)

   null (Ed.)
2. Homotopy, homology, and persistent homology using closure spaces

   https://doi.org/10.1007/s41468-024-00183-8  

   Bubenik, Peter; Milićević, Nikola (July 2024, Journal of Applied and Computational Topology)

   Abstract. We develop persistent homology in the setting of filtrations of (Cˇech) closure spaces. Examples of filtrations of closure spaces include metric spaces, weighted graphs, weighted directed graphs, and filtrations of topological spaces. We use various products and intervals for closure spaces to obtain six homotopy theories, six cubical singular homology theories, and three simplicial singular homology theories. Applied to filtrations of closure spaces, these homology theories produce persistence modules. We extend the definition of Gromov-Hausdorff distance from metric spaces to filtrations of closure spaces and use it to prove that any persistence module obtained from a homotopy-invariant functor on closure spaces is stable. 

   more » « less
3. Topological coHochschild homology and the homology of free loop spaces

   https://doi.org/10.1007/s00209-021-02879-4  

   Bohmann, Anna Marie; Gerhardt, Teena; Shipley, Brooke (May 2022, Mathematische Zeitschrift)
4. Quantum persistent homology

   https://doi.org/10.1007/s41468-023-00160-7  

   Ameneyro, Bernardo; Maroulas, Vasileios; Siopsis, George (January 2024, Journal of Applied and Computational Topology)
5. Ribbon homology cobordisms

   https://doi.org/10.1016/j.aim.2022.108580  

   Daemi, Aliakbar; Lidman, Tye; Vela-Vick, David Shea; Wong, C.-M. Michael (October 2022, Advances in Mathematics)