2014/05/27 by Alexander Kupers, Jeremy Miller, Kupers, Alexander +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #55P48 #55R40 #55R80 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Microtubule and mitosis dynamics #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1405.7087
openalex publication_date 2014/05/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We define bounded generation for En-algebras in chain complexes and prove that for n ≥ 2 this property is equivalent to homological stability. Using this we prove a local-to-global principle for homological stability, which says that if an En-algebra A has homological stability (or equivalently the topological chiral homology ∫Rn A has homology stability), then so has the topological chiral homology ∫M A of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle in a way that also applies to compact manifolds. We also give several applications of our results