2020/03/09 by Chachólski, Wojciech, Giunti, Barbara, Landi, Claudia · 2 citations
#55N31 #55PXX #Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.03969
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.