29 citations · 54 across the 13 of their papers we have counts for
20 papers
Choosing the Geometry: valuations, norms, and contours
Jens Agerberg, Wojciech Chachólski, Christina Kapatsori
We develop a general framework for constructing pseudometrics on objects of Abelian categories using valuations, which assign non-negative costs to morphisms. Specializing to finit…
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…
Data, geometry and homology
Jens Agerberg, Wojciech Chacholski, Ryan Ramanujam
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we inves…
Realisations of posets and tameness
Wojciech Chacholski, Alvin Jin, Francesca Tombari
We introduce a construction called realisation which transforms posets into posets. We show that realisations share several key features with upper semilattices. For example, we de…
Homotopical decompositions of simplicial and Vietoris Rips complexes
Wojciech Chacholski, Alvin Jin, Martina Scolamiero +1
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of suc…
Landscapes of data sets and functoriality of persistent homology
Wojciech Chacholski, Alessandro De Gregorio, Nicola Quercioli +1
The aim of this article is to describe a new perspective on functoriality of persistent homology and explain its intrinsic symmetry that is often overlooked. A data set for us is a…
On the topology of complexes of injective words
Wojtek Chacholski, Ran Levi, Roy Meshulam
An injective word over a finite alphabet is a sequence of distinct elements of . The set of injective words on is partially ordere…
A topological data analysis based classification method for multiple measurements
Henri Riihimäki, Wojciech Chachólski, Jakob Theorell +2
Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data…
Metrics and stabilization in one parameter persistence
Wojciech Chachólski, Henri Riihimäki
We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played…
Generalized persistence analysis based on stable rank invariant
Henri Riihimäki, Wojciech Chacholski
We believe three ingredients are needed for further progress in persistence and its use: invariants not relying on decomposition theorems to go beyond 1-dimension, outcomes suitabl…
Relative homological algebra via truncations
Wojciech Chacholski, Amnon Neeman, Wolfgang Pitsch +1
To do homological algebra with unbounded chain complexes one needs to first find a way of constructing resolutions. Spaltenstein solved this problem for chain complexes of R-module…
Multidimensional Persistence and Noise
Martina Scolamiero, Wojciech Chachólski, Anders Lundman +2
In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the categor…
Combinatorial presentation of multidimensional persistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
A multifiltration is a functor indexed by that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the na…
Homotopy excision and cellularity
Wojciech Chacholski, Jerome Scherer, Kay Werndli
Consider a push-out diagram of spaces C <-- A --> B, construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object A. We…
Homotopy colimits of nilpotent spaces
Wojciech Chacholski, Emmanuel Dror Farjoun, Ramon Flores +1
We show that cellular approximations of nilpotent Postnikov stages are always nilpotent Postnikov stages, in particular classifying spaces of nilpotent groups are turned into class…
On the classification of fibrations
Martin Blomgren, Wojciech Chacholski
Classification questions are often about understanding components of a category. It is much more desirable however to be able to understand the entire homotopy type of this categor…
Combinatorial resolutions of multigraded modules and multipersistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
Let and a multigraded module. In this work we interpret as a multipersistent homology module and give a multigraded resolution of it. The construction…
Homotopy exponents for large H-spaces
Wojciech Chacholski, Wolfgang Pitsch, Jerome Scherer +1
We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive…
Representations of Spaces
W. Chacholski, J. Scherer
We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and…
Homotopy pull-back squares up to localization
W. Chacholski, W. Pitsch, J. Scherer
We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps c…