14 citations · 14 across the 2 of their papers we have counts for
6 papers
Dowker's theorem for higher-order relations
Vin de Silva, Chad Giusti, Vladimir Itskov +5
Given a relation between two sets, Dowker's Theorem (1952) states that the homology groups of two associated simplicial complexes, now known as Dowker comp…
Parametrized Homology via Zigzag Persistence
Gunnar Carlsson, Vin de Silva, Sara Kalisnik +1
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding…
The observable structure of persistence modules
Frederic Chazal, William Crawley-Boevey, Vin de Silva
In persistent topology, q-tame modules appear as a natural and large class of persistence modules indexed over the real line for which a persistence diagram is definable. However,…
Persistence stability for geometric complexes
Frederic Chazal, Vin de Silva, Steve Oudot
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris-Rips, Cech and witness complexes) built on top of precompact space…
Combinatorial Floer Homology
Vin de Silva, Joel Robbin, Dietmar Salamon
We define combinatorial Floer homology of a transverse pair of noncontractibe nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant unde…
Dualities in persistent (co)homology
Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their p…