E _n-cell attachments and a local-to-global principle for homological stability

TY - JOUR

T1 - E n-cell attachments and a local-to-global principle for homological stability

AU - Kupers, Alexander

AU - Miller, Jeremy

PY - 2018/2/1

Y1 - 2018/2/1

N2 - We define bounded generation for En -algebras in chain complexes and prove that this property is equivalent to homological stability for n≥2 . 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 ∫RnA has homology stability), then so has the topological chiral homology ∫MA of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle so that it applies to compact manifolds. We also give several applications of our results.

AB - We define bounded generation for En -algebras in chain complexes and prove that this property is equivalent to homological stability for n≥2 . 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 ∫RnA has homology stability), then so has the topological chiral homology ∫MA of any connected non-compact manifold M. Using scanning, we reformulate the local-to-global homological stability principle so that it applies to compact manifolds. We also give several applications of our results.

U2 - 10.1007/s00208-017-1533-3

DO - 10.1007/s00208-017-1533-3

M3 - Journal article

SN - 0025-5831

VL - 370

SP - 209

EP - 269

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 1-2

ER -