Whitehead torsion and the kernel of assembly
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914494472519680 |
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| author | Harr, Oscar |
| author_facet | Harr, Oscar |
| contents | For a topological space that is homeomorphic to a finite simplicial complex, we prove that the Bartels--Nikolaus assembly functor has a fully faithful right adjoint. Using this, we define for each such topological space $X$ a {\em Whitehead category}, whose K-theory is canonically identified with the Whitehead spectrum of $X$; and for a homotopy equivalence between two such spaces, we define an object in the Whitehead category of $X$ called the {\em torsion cosheaf} of the map, whose K-theory class recovers the classical Whitehead torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19208 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Whitehead torsion and the kernel of assembly Harr, Oscar Algebraic Topology Geometric Topology For a topological space that is homeomorphic to a finite simplicial complex, we prove that the Bartels--Nikolaus assembly functor has a fully faithful right adjoint. Using this, we define for each such topological space $X$ a {\em Whitehead category}, whose K-theory is canonically identified with the Whitehead spectrum of $X$; and for a homotopy equivalence between two such spaces, we define an object in the Whitehead category of $X$ called the {\em torsion cosheaf} of the map, whose K-theory class recovers the classical Whitehead torsion. |
| title | Whitehead torsion and the kernel of assembly |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2604.19208 |