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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Monopole Maps and L² -cohomology
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Monopole Maps and L² -cohomology
Tsuyoshi Kato, Nobuhiro Nakamura (Gebundene Ausgabe, Englisch)
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Beschreibung
The theme of this book is to establish a link between gauge theory and L ²-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 L ²-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 L ²-cohomology, L ²-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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
26.08.2025
Sprache
Englisch
EAN
9789819684717
Herausgeber
Springer Singapore
Serien- oder Bandtitel
Springer Monographs in Mathematics
Sonderedition
Nein
Autor
Tsuyoshi Kato, Nobuhiro Nakamura
Seitenanzahl
292
Einbandart
Gebundene Ausgabe
Schlagwörter
Seiberg-Witten theory, Bauer-Furuta theory, L² cohomology theory, 11/8-conjecture, Singer conjecture
Thema-Inhalt
PBP - Topologie
PBMP - Differentielle und Riemannsche Geometrie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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