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math.AT2023
Ladder Decomposition for Morphisms of Persistence Modules
Živa Urbančič, Jeffrey Giansiracusa
The output of persistent homology is an algebraic object called a persistence module. This object admits a decomposition into a direct sum of interval persistence modules described…
math.AT2019
Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem
Jeffrey Giansiracusa, Alexander Kupers, Bena Tshishiku
Let be the K3 manifold. In this note, we discuss two methods to prove that certain generalized Miller--Morita--Mumford classes for smooth bundles with fiber are non-zero. A…
math.AT2007★ 5 cited
Pontrjagin-Thom maps and the homology of the moduli stack of stable curves
Johannes Ebert, Jeffrey Giansiracusa
We study the singular homology (with field coefficients) of the moduli stack of stable n-pointed complex curves of genus g (the Deligne-Mumford compactification). Each of its irred…