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Secondary homological stability and periodic homological stability for unordered configuration spaces

Ponente: Zachary Himes
Institución: Purdue University
 Tipo de Evento: Investigación
Cuándo 14/06/2022
de 16:00 a 17:30
Dónde En linea (zoom)
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Nota. Ésta es una sesión especial del seminario: el horario, la duración y el enlace de Zoom son diferentes de lo usual (el enlace será enviado a la lista de correos).
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary stability for unordered configuration spaces of manifolds. The main difficulty is the compact case (the non-compact case was previously known by some experts). In the compact case, there are no obvious stabilization maps and the homology does not stabilize but is periodic.  We resolve this issue by constructing a chain-level stabilization map for configuration spaces of compact manifolds.