Controlled objects in left-exact ∞-categories and the Novikov conjecture

2019/11/06 by Ulrich Bunke, Denis-Charles Cisinski, Bunke, Ulrich +5 · 3 citations
Mathematics · Medicine · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #K-Theory and Homology (math.KT) #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1911.02338

openalex publication_date 2019/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We associate to every G-bornological coarse space X and every left-exact ∞-category with G-action a left-exact infinity-category of equivariant X-controlled objects. Postcomposing with algebraic K-theory leads to new equivariant coarse homology theories. This allows us to apply the injectivity results for assembly maps by Bunke, Engel, Kasprowski and Winges to the algebraic K-theory of left-exact ∞-categories.

Citations

• Synthetic spectra and the cellular motivic category

Cited by

• The weight filtration on real singular homology is motivic
• Localisation theorems for the connective K-theory of exact categories
• Deligne 1-motives with torsion and étale motives

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