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Abstract
We study the assembly map on
K TC
S + 1 ∧
K ( 𝕊 )
→
K ( 𝕊 [ x ± 1 ] ) and S
+ 1 ∧ TC ( 𝕊 )
→ TC ( 𝕊 [ x ± 1 ] ) .
In the second case we are able to describe geometrically what the cofiber is. Using
this we show that the Whitehead space of the circle has a countable sum of
Ω ∞ coker ( j ) p ∧
Keywords
$K\mkern-2mu$-theory, topological cyclic homology, trace
methods, Whitehead spectrum
Mathematical Subject Classification
Primary: 19D10
Secondary: 19D55, 55P91
Milestones
Received: 4 February 2023
Revised: 17 May 2024
Accepted: 10 June 2025
Published: 21 July 2025
© 2025 MSP (Mathematical Sciences
Publishers).
