Téléchargez le livre : Monopole Maps and L² -cohomology
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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.
Pages
292 pages
Collection
n.c
Parution
2025-08-25
Marque
Springer
EAN papier
9789819684717
EAN PDF
9789819684724
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
29
Taille du fichier
5325 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
158,24 €
EAN EPUB
9789819684724
Informations sur l'ebook
Nombre pages copiables
2
Nombre pages imprimables
29
Taille du fichier
20163 Ko
Ce livre est accessible aux handicaps Voir les informations sur l'accessibilité
Prix
158,24 €

Tsuyoshi Kato received his Ph.D. from Kyoto University in 1995. He is currently a Professor of Mathematics at Kyoto University.

Nobuhiro Nakamura received his Ph.D. from Kyoto University in 2006. He is currently a Professor of Mathematics at Fukushima Medical University.

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