國立虎尾科技大學 |

Monopole Maps and L² -Cohomology

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Monopole Maps and L² -Cohomology/ by Tsuyoshi Kato, Nobuhiro Nakamura.
作者:	Kato, Tsuyoshi.
其他作者:	Nakamura, Nobuhiro.
出版者:	Singapore :Springer Nature Singapore : : 2025.,
面頁冊數:	xix, 292 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential topology. -
電子資源:	https://doi.org/10.1007/978-981-96-8472-4
ISBN:	9789819684724

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

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

527678
Differential topology.

LC Class. No.: QA613.6

Dewey Class. No.: 514.72

Monopole Maps and L² -Cohomology
LDR:02681nam a2200325 a 4500 001 1166544
003 DE-He213
005 20250826130150.0
006 m d
007 cr nn 008maaau
008 251217s2025 si s 0 eng d
020 $a 9789819684724 $q (electronic bk.)
020 $a 9789819684717 $q (paper)
024 7 $a 10.1007/978-981-96-8472-4 $2 doi
035 $a 978-981-96-8472-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA613.6
072 7 $a PBP $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBP $2 thema
082 0 4 $a 514.72 $2 23
090 $a QA613.6 $b .K19 2025
100 1 $a Kato, Tsuyoshi. $3 1495327
245 1 0 $a Monopole Maps and L² -Cohomology $h [electronic resource] / $c by Tsuyoshi Kato, Nobuhiro Nakamura.
260 $a Singapore : $c 2025. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xix, 292 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
520 $a 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.
650 0 $a Differential topology. $3 527678
650 0 $a Homology theory. $3 682984
650 1 4 $a Topology. $3 633483
650 2 4 $a Differential Geometry. $3 671118
700 1 $a Nakamura, Nobuhiro. $3 1495328
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 882184
856 4 0 $u https://doi.org/10.1007/978-981-96-8472-4
950 $a Mathematics and Statistics (SpringerNature-11649)