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- Tags
- Refs:
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Links:
- THH
- scanning map
- nonabelian Poincare duality
- Dold-Thom theorem
- cobordism hypothesis
factorization homology
Motivations
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Motivations: factorization homology forms an important class of topological field theories: the ones in which the global observables are determined by the local observables. It can be modeled using labeled configuration spaces; in fact, it originates from configuration space models for mapping spaces.
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Descriptions of the factorization homology of free E_n algebra and of \(E_n{\hbox{-}}\)enveloping algebras of Lie algebras are known.
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suspension spectra provide another class of algebras for which factorization homology is known.
- This follows from nonabelian Poincare duality: describes factorization homology of \(n\)-fold loop spaces in terms of mapping spaces or section spaces.
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For \(M = S^1\) , factorization homology specializes to Topological Hochschild homology.
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There is an equivalence of categories \begin{align*} {}_{E_1{\hbox{-}}A}{\mathsf{Mod}} \cong ({A}, {A}){\hbox{-}}\mathsf{biMod}.\end{align*}
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Definitions
Examples
