Muutke küpsiste eelistusi

E-raamat: Locally Mixed Symmetric Spaces

Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 172,28 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Locally Mixed Symmetric SpacesSuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology.

Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry.

Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Arvustused

The book contains a very useful index. As a global view, we must mention that most of the results are given with their complete proofs; this fact increases the value of the book and makes it an excellent scientific material for the researchers in the field. Besides the valuable contents, the topics being of high interest for specialists in topology, algebraic and differential geometry, one must remark once more the very well organization and clarity of this monograph. (Adela-Gabriela Mihai, zbMATH 1504.53001, 2023)

1 Symmetric Spaces
1(178)
1.1 Homogeneous Spaces
2(22)
1.1.1 Invariant Connections
2(6)
1.1.2 Compact Homogeneous Spaces
8(5)
1.1.3 Complex Homogeneous Spaces
13(4)
1.1.4 Projective Embeddings
17(6)
1.1.5 Non-compact Homogeneous Spaces
23(1)
1.2 Symmetric Spaces
24(31)
1.2.1 Globally Symmetric Spaces
24(4)
1.2.2 Isometries
28(2)
1.2.3 Dualities
30(3)
1.2.4 Locally Symmetric Spaces
33(1)
1.2.5 Examples
34(9)
1.2.6 Riemannian Symmetric Spaces
43(12)
1.3 Classification of Symmetric Spaces
55(15)
1.3.1 Symmetric Lie Algebras
55(10)
1.3.2 Structure of Symmetric Spaces
65(5)
1.4 Symmetric Subpairs and Totally Geodesic Subspaces
70(3)
1.5 Hermitian Symmetric Spaces
73(40)
1.5.1 Compact Hermitian Symmetric Spaces
74(12)
1.5.2 Non-compact Hermitian Symmetric Spaces
86(10)
1.5.3 The Exceptional Domains
96(3)
1.5.4 Cayley Transforms
99(2)
1.5.5 Boundary Components
101(7)
1.5.6 Appendix: Siegel Domains
108(5)
1.6 Examples
113(27)
1.6.1 The Poincare Plane
113(2)
1.6.2 Hyperbolic Spaces
115(7)
1.6.3 Some Symmetric Spaces Arising from Exceptional Groups
122(2)
1.6.4 Symmetric Spaces Related to SU (4)
124(1)
1.6.5 Hermitian Symmetric Spaces of Grassmann Type
125(4)
1.6.6 Projective Planes
129(11)
1.7 Satake Compactifications
140(21)
1.7.1 Compactifications
141(3)
1.7.2 Borel--Serre Compactification
144(3)
1.7.3 The Compactification Pn of Pn = SLn(C)/SU(n)
147(3)
1.7.4 Satake Compactifications
150(11)
1.8 Morse Theory and Symmetric Spaces
161(18)
1.8.1 Generalizations of Morse Theory
161(2)
1.8.2 Applications of Morse Theory to Symmetric Spaces
163(6)
1.8.3 The Space of Loops
169(10)
2 Locally Symmetric Spaces
179(142)
2.1 Arithmetic Quotients
181(10)
2.1.1 Commensurability
182(3)
2.1.2 Classification of Arithmetic Groups (Examples)
185(6)
2.2 Rational Boundary Components
191(12)
2.2.1 The theorem of GauB-Bonnet for Arithmetic Quotients
194(9)
2.3 Compactifications of Arithmetic Quotients
203(11)
2.3.1 Borel-Serre Compactification
203(3)
2.3.2 Satake Compactifications
206(8)
2.4 Locally Hermitian Symmetric Spaces
214(17)
2.4.1 Rational Boundary Components
215(1)
2.4.2 Baily-Borel Embedding
216(2)
2.4.3 Toroidal Compactifications of Locally Hermitian Symmetric Varieties
218(13)
2.5 The Proportionality Principle
231(8)
2.5.1 Hirzebruch Proportionality in the Non-compact Case
234(5)
2.6 Locally Symmetric Subspaces; Totally Geodesic Subspaces
239(12)
2.6.1 Geodesic Cycles
240(3)
2.6.2 Non-vanishing (Co-)Homology
243(3)
2.6.3 Relative Proportionality
246(5)
2.7 Examples
251(65)
2.7.1 Spaces Deriving from Geometric Forms
252(7)
2.7.2 The Poincare Plane
259(9)
2.7.3 Hyperbolic 3-Folds
268(8)
2.7.4 Picard Modular Varieties (Arithmetic Quotients of Complex Hyperbolic Manifolds)
276(12)
2.7.5 Hyperbolic D-Planes
288(11)
2.7.6 Arithmetic Quotients of Hermitian Symmetric Spaces of Grassmann Type
299(13)
2.7.7 Janus-Like Algebraic Varieties
312(4)
2.8 Locally Semisimple Symmetric Spaces
316(5)
3 Locally Mixed Symmetric Spaces
321(54)
3.1 Mixed Symmetric Spaces
322(9)
3.1.1 Mixed Symmetric Pairs
322(1)
3.1.2 Morphisms of Mixed Symmetric Pairs
323(6)
3.1.3 Extensions of Mixed Symmetric Spaces to Compactifications
329(2)
3.2 Locally Mixed Symmetric Spaces
331(11)
3.2.1 Structure of the Fiber
339(3)
3.3 Examples
342(16)
3.3.1 Examples Deriving from Geometric Forms
342(8)
3.3.2 Examples Arising from Exceptional Groups
350(8)
3.4 Locally Mixed Symmetric Spaces and Compactifications
358(7)
3.4.1 LMSS and the Borel-Serre Compactification
358(4)
3.4.2 Embedding Locally Symmetric Spaces in Larger Ones
362(3)
3.5 Global Sections
365(10)
4 Kuga Fiber Spaces
375(112)
4.1 Period Domains
376(30)
4.1.1 Hodge Structures
376(5)
4.1.2 Variation of Hodge Structures
381(4)
4.1.3 Monodromy
385(9)
4.1.4 Hodge Structures of Weight 2
394(12)
4.2 Hodge Structures of Weight 1
406(19)
4.2.1 Complex Tori
406(2)
4.2.2 Siegel Spaces
408(6)
4.2.3 Families of Abelian Varieties
414(11)
4.3 Kuga Fiber Spaces
425(6)
4.3.1 LMSS of Hermitian Type
425(1)
4.3.2 Kuga Fiber Spaces
426(1)
4.3.3 Polarized Hodge Structures of Weight 1
427(1)
4.3.4 Characterization of Kuga Fiber Spaces
428(3)
4.4 Symplectic Representations of Q-Groups
431(18)
4.4.1 Hermitian Forms, Symplectic Forms and Involutions
431(1)
4.4.2 Holomorphic Embeddings of Symmetric Domains into a Siegel Space
432(11)
4.4.3 Classification of Kuga Fiber Spaces
443(6)
4.5 Pel Structures and Equivariant Embeddings
449(2)
4.6 Modular Subvarieties, Boundary Components and Degenerations
451(14)
4.6.1 Decompositions
451(2)
4.6.2 Degenerations
453(5)
4.6.3 Namikawa's Compactification
458(7)
4.7 Examples
465(18)
4.7.1 Hodge Structures of Weight 2
466(1)
4.7.2 Families of Abelian Varieties with Real Multiplication
467(1)
4.7.3 Families of Abelian Varieties with Complex Multiplication
467(5)
4.7.4 Families of Abelian Varieties with Quaternion Multiplication
472(1)
4.7.5 Hyperbolic D-Planes
472(5)
4.7.6 A Ball Quotient Related to a Division Algebra
477(6)
4.8 Group of Sections
483(4)
5 Elliptic Surfaces
487(56)
5.1 Elliptic Curves
489(2)
5.2 Elliptic Surfaces
491(3)
5.3 Singular Fibers
494(4)
5.4 Homological and Functional Invariants
498(2)
5.5 The Family of Elliptic Surfaces with Given Invariants
500(9)
5.6 Numerical Invariants of Elliptic Surfaces
509(8)
5.7 The Exponential Sequence
517(5)
5.8 Elliptic Modular Surfaces
522(8)
5.9 The Classifying Map of an Elliptic Surface
530(3)
5.10 Weierstraß Models
533(3)
5.11 Deformations and Moduli
536(5)
5.12 Appendix: Curves on a Compact Complex Surface
541(2)
6 Appendices
543(74)
6.1 Algebra
543(8)
6.1.1 Geometric Forms
543(3)
6.1.2 A--Algebras
546(1)
6.1.3 Division Algebras
547(4)
6.2 Topology and Differential Geometry
551(16)
6.2.1 Homotopy, Classifying Spaces and Fiber Bundles
551(2)
6.2.2 Leray-Hirsch Theorem
553(1)
6.2.3 Characteristic Classes
554(2)
6.2.4 Differential Geometry
556(3)
6.2.5 Lie Groups and Lie Algebras
559(8)
6.3 Complex Geometry and Algebraic Groups
567(13)
6.3.1 Complex Manifolds and Algebraic Varieties
568(3)
6.3.2 Hodge Structures
571(2)
6.3.3 Abelian Varieties
573(2)
6.3.4 Algebraic Groups
575(2)
6.3.5 Arithmetic Groups
577(3)
6.4 Exceptional Algebraic and Lie Groups
580(14)
6.4.1 Real Lie Groups
580(1)
6.4.2 Octonions
581(3)
6.4.3 Jordan Algebras
584(3)
6.4.4 Exceptional Lie Algebras
587(7)
6.5 Some Finite Geometry
594(5)
6.5.1 Isotropic Subspaces
594(2)
6.5.2 Non-degenerate Subspaces
596(1)
6.5.3 The Index of PΓ(N) in PSp2g(Z)
597(2)
References
599(18)
Index 617
Bruce Hunt studied at the University of Bonn (1978­1983) and obtained his PhD from the Max Planck Institute für Mathematik in 1986 under Fr. Hirzebruch and Andrew Sommese. From 1987 to 2000 he was Assistant Professor at Purdue University, Göttingen, Kaiserslautern, and the Max Planck Institute. Since 2000 he has worked in international investment banks, in trading architecture and risk control.
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97830306980412e.html
Märksõnad: