We consider the question of defining interleaving metrics on generalized persistence
modules over arbitrary preordered sets. Our constructions are functorial, which implies a …

We construct “barcodes” for the chain complexes over Novikov rings that arise in Novikov's
Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone …

This paper introduces parametrized homology, a continuous-parameter generalization of
levelset zigzag persistent homology that captures the behavior of the homology of the fibers …

We introduce a sheaf-theoretic stability condition for finite acyclic quivers. Our main result
establishes that for representations of affine type A˜ quivers, there is a precise relationship …

This book is about new topological invariants of real-and angle-valued maps inspired by
Morse-Novikov theory, a chapter of topology, which has recently raised interest outside of …

We develop a general algebraic framework involving" Poincar\'e--Novikov structures" and"
filtered matched pairs" to provide an abstract approach to the barcodes associated to the …

A periodic cell complex, $ K $, has a finite representation as the quotient space, $ q (K) $,
consisting of equivalence classes of cells identified under the translation group acting on $ K …

We propose a refinement of the Betti numbers and the homology with coefficients in a field of
a compact ANR X, in the presence of a continuous real-valued function on X. The refinement …

We prove that pointwise finite-dimensional S^ 1 persistence modules over an arbitrary field
decompose uniquely, up to isomorphism, into the direct sum of a bar code and finitely-many …

In this paper we consider the definition of" monodromy of an angle valued map" based on
linear relations as proposed in Burghelea-Haller (3). This definition provides an alternative …