Factoring the Becker-Gottlieb Transfer Through the Trace Map

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。

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

We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by indep…

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…

The transfer map of free loop spaces

For any perfect fibration $E \rightarrow B$, there is a "free loop transfer map" $LB_+ \rightarrow LE_+$, defined using topological Hochschild homology. We prove that this transfer is compatible with the Becker-Gottlieb transfer, allowing us to extend a result of Dorabiała and Johnson on the transfer map in Waldhausen's $A$-theory. In the case where $E \rightarrow B$ is a smooth fiber bundle, we also give a concrete geometric model for the free loop transfer in terms of Pontryagin-Thom collapse maps. We recover the previously known computations of the free loop transfer due to Schlichtkrull, a…