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Title: Topological coHochschild homology and the homology of free loop spaces
Award ID(s):
1811278 1810575 1710534 2104300
PAR ID:
10331920
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Mathematische Zeitschrift
Volume:
301
Issue:
1
ISSN:
0025-5874
Page Range / eLocation ID:
411 to 454
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  2. 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. 
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