#cohomology
10 papers · 1 filter
Interval Decompositions for Multipersistence Modules over Finite Posets and Robustness of Sheaf Data on Simplicial Complexes
Pablo Hernández-GarcÃa, Daniel Hernández Serrano, DarÃo Sánchez Gómez
The paper establishes conditions under which multipersistence modules indexed by finite posets can be broken down into direct sums of interval modules, and applies these results to…
Phase Retrieval in Requires Exactly Eleven Measurements
Meng Huang
The paper proves that exactly eleven intensity measurements are needed for phase retrieval in four-dimensional complex space, settling the minimal measurement count and its implica…
Algebraic paradoxes in adaptive quantum computation
Samson Abramsky, Rui Soares Barbosa, Carmen Constantin +1
The paper shows that any adaptive Z₂‑linear measurement‑based quantum computation that deterministically computes a non‑affine Boolean function must involve a quantum resource that…
Bosonic SPT and invertible phases and its relation to Steenrod's problem
Shota Saito, Yuji Tachikawa, Yi Zhang
The paper systematically studies bosonic invertible and symmetry‑protected topological phases, showing that beyond‑cohomology phenomena first appear as a mod‑3 effect and linking t…
Non-abelian extensions of Hom-Jacobi-Jordan algebras
Nejib Saadaoui
The paper develops a cohomology theory for Hom‑Jacobi‑Jordan algebras and shows that split non‑abelian extensions of such algebras are classified by the second cohomology group.
Homotopy of representations up to homotopy
Olivier Brahic, Pedro Frejlich
The paper defines morphisms between representations up to homotopy of Lie algebroids and shows that their cohomology behaves functorially, preserving homotopy invariance and local…