Differential function spectra, the differential Becker-Gottlieb transfer, and applications to differential algebraic K-theory / Ulrich Bunke, David Gepner.

Format:

Book

Author/Creator:

Bunke, Ulrich, 1963- author.

Gepner, David, author.

Series:

Memoirs of the American Mathematical Society ; no. 1316.

Memoirs of the American Mathematical Society ; number 1316

Language:

English

Subjects (All):

Differential topology.

K-theory.

Physical Description:

v, 177 pages : illustrations ; 26 cm.

Place of Publication:

Providence : American Mathematical Society, [2021]

Summary:

"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 independent means."--publisher supplied abstract.

Contents:

Introduction

Differential function spectra

Cycle maps

Transfers in differential cohomology

A transfer index conjecture

Technicalities

Bibliography.

Notes:

"January 2021, volume 269, number 1316 (seventh of 7 numbers)"--Cover.

Includes bibliographical references.

ISBN:

1470446855

9781470446857

OCLC:

1260683709