The transfer is functorial

On transfer maps in the algebraic K-theory of spaces

“…In Sect. 3, we first recall the definition and some properties of the A-theory transfer maps and state the theorems of Lind-Malkiewich [9] and Klein-Malkiewich [8]. Combining these results, we obtain an identification of the map (3) in terms of Becker-Gottlieb transfer maps (Corollary 3.5) and then prove Theorem 3.7.…”

“…Obtaining such a refinement of Theorem 3.7 essentially depends on the naturality properties of the homotopy for the functoriality of the Becker-Gottlieb transfer maps in Theorem 3.6. We do not know whether the necessary naturality properties hold for the homotopy shown in [8]. On the other hand, we also hope that an altogether different approach to Question (1) might be possible.…”

“…Special cases of this result were also shown in [2,3] using different methods. We refer to [1,5,8] for the definition and properties of the Becker-Gottlieb transfer maps.…”

“…in terms of Becker-Gottlieb transfer maps (Corollary 3.5). Finally, using this identification of (3), the proof of Theorem 3.7 is reduced to the functoriality of the Becker-Gottlieb transfer maps shown by Klein-Malkiewich [8] (stated in (C)).…”

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

“…in terms of Becker-Gottlieb transfer maps (Corollary 3.5). Finally, using this identification of (3), the proof of Theorem 3.7 is reduced to the functoriality of the Becker-Gottlieb transfer maps shown by Klein-Malkiewich [7] (stated in (C)).…”