Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory

Becker–Gottlieb转移不是函子：基于群环单位的一个例子

The Becker--Gottlieb transfer is not functorial: An example based on units of group rings

该研究通过明确反例证明Becker–Gottlieb转移无法成为函子，还提及同期发现的另一反例，为相关理论提供了关键反证。

Factoring the Becker-Gottlieb Transfer Through the Trace Map

We verify the Becker-Shultz axioms characterizing the Becker-Gottlieb transfer $τ$ for the composite of the algebraic K-theory transfer of any perfect fibration followed by the trace map. As a consequence, for any compact ANR fibration (those considered by Becker-Shultz), $τ$ is homotopy equivalent to the composite of the algebraic K-theory transfer followed by the trace map. Furthermore, if these same axioms (including strong additivity) could be shown to extend to characterizing $τ$ for arbitrary perfect fibrations, our homotopy equivalence extends to the case of arbitrary perfect fibrations…

Becker-Gottlieb转移不具有函子性：一个使用$C_\infty$-代数的例子

The Becker-Gottlieb transfer is not functorial: An example using $C_\infty$-algebras

该研究证明Becker-Gottlieb转移不具有函子性，通过构造特定纤维化与定向$S^1$-丛，结合有理模型给出反例，还提供了基于$C_\infty$-代数模型的补充证明。

On transfer maps in the algebraic $K$-theory of spaces

We show that the Waldhausen trace map $\mathrm{Tr}_X \colon A(X) \to QX_+$, which defines a natural splitting map from the algebraic $K$-theory of spaces to stable homotopy, is natural up to \emph{weak} homotopy with respect to transfer maps in algebraic $K$-theory and Becker-Gottlieb transfer maps respectively.

The refined transfer, bundle structures and algebraic K-theory

We give new homotopy theoretic criteria for deciding when a fibration with homotopy finite fibers admits a reduction to a fiber bundle with compact topological manifold fibers. The criteria lead to a new and unexpected result about homeomorphism groups of manifolds. A tool used in the proof is a surjective splitting of the assembly map for Waldhausen's functor A(X). We also give concrete examples of fibrations having a reduction to a fiber bundle with compact topological manifold fibers but which fail to admit a compact fiber smoothing. The examples are detected by algebraic K-theory invariant…

纤维化THH转移的有理模型 I：Sullivan代数

A rational model for the fiberwise THH transfer I: Sullivan algebras

本文证明纤维化THH转移可由Sullivan模型的Hochschild同调转移理性建模，通过高阶范畴追踪理论和Braunack-Mayer的工作实现。