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Monopole Maps and L² -Cohomology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Monopole Maps and L² -Cohomologyby Tsuyoshi Kato, Nobuhiro Nakamura.
Author:	Kato, Tsuyoshi.
other author:	Nakamura, Nobuhiro.
Published:	Singapore :Springer Nature Singapore :2025.
Description:	xix, 292 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential topology.
Online resource:	https://doi.org/10.1007/978-981-96-8472-4
ISBN:	9789819684724$q(electronic bk.)

Monopole Maps and L² -Cohomology
Kato, Tsuyoshi.

Monopole Maps and L² -Cohomology[electronic resource] /by Tsuyoshi Kato, Nobuhiro Nakamura. - Singapore :Springer Nature Singapore :2025. - xix, 292 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

The theme of this book is to establish a link between gauge theory and L²-cohomology theory. Although both theories focus on differential topology, they have been developed rather independently. One of the main reasons lies in the differing characteristics of these theories. This book introduces an integrated theory that bridges these subjects. One goal of the book is to propose differential-topological conjectures that are covering versions of the so-called 10/8-theorem. We include various pieces of evidence to support them. This book is almost self-contained and is accessible not only to graduate students in differential geometry but also to both the experts in L²-cohomology theory and gauge theory. This unique and fundamental book contains numerous unsolved problems, suggesting future directions of topology of smooth 4-manifolds by using various analytic methods. After the introduction (Chap. 1), Chap. 2 gives a quick overview of the historical progress of differential topology. Chap. 3 covers the basic subjects of spin geometry. Chaps 4 and 5 deal with the foundations of the Seiberg-Witten and the Bauer-Furuta theories. In Chaps 6 and 7, we present the basic theory of L²-cohomology, L²-Betti numbers, amenability, and residual finiteness of discrete groups. In Chap. 8, we treat the Singer conjecture and describe the solution to the conjecture for Kähler hyperbolic manifolds. We then describe various variations of Furuta's 10/8-inequalities and how the aspherical 10/8-inequalities conjecture is induced. We provide the evidence by examining various classes of 4-manifolds, such as aspherical surface bundles and complex surfaces.

ISBN: 9789819684724$q(electronic bk.)

Standard No.: 10.1007/978-981-96-8472-4doiSubjects--Topical Terms:

212318
Differential topology.

LC Class. No.: QA613.6

Dewey Class. No.: 514.72

Monopole Maps and L² -Cohomology
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