E n-cell attachments and a local-to-global principle for homological stability
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E n-cell attachments and a local-to-global principle for homological stability. / Kupers, Alexander; Miller, Jeremy.
In: Mathematische Annalen, Vol. 370, No. 1-2, 2018, p. 209-269.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - E n-cell attachments and a local-to-global principle for homological stability
AU - Kupers, Alexander
AU - Miller, Jeremy
PY - 2018
Y1 - 2018
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
VL - 370
SP - 209
EP - 269
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1-2
ER -
ID: 222542966