LEADER 04106nam 2200613Ia 450 001 9910785918503321 005 20230801225126.0 010 $a1-283-63598-4 010 $a981-4412-26-0 035 $a(CKB)2670000000272702 035 $a(EBL)1044407 035 $a(OCoLC)811820797 035 $a(SSID)ssj0000682586 035 $a(PQKBManifestationID)11405009 035 $a(PQKBTitleCode)TC0000682586 035 $a(PQKBWorkID)10696058 035 $a(PQKB)10708639 035 $a(MiAaPQ)EBC1044407 035 $a(WSP)00002801 035 $a(Au-PeEL)EBL1044407 035 $a(CaPaEBR)ebr10607776 035 $a(CaONFJC)MIL394844 035 $a(EXLCZ)992670000000272702 100 $a20120605d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry of crystallographic groups$b[electronic resource] /$fAndrzej Szczepan?ski 210 $aHackensack, NJ $cWorld Scientific$d2012 215 $a1 online resource (208 p.) 225 0 $aAlgebra and discrete mathematics ;$vv. 4 300 $aDescription based upon print version of record. 311 $a981-4412-25-2 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; 1. Definitions; 1.1 Exercises; 2. Bieberbach Theorems; 2.1 The first Bieberbach Theorem; 2.2 Proof of the second Bieberbach Theorem; 2.2.1 Cohomology group language; 2.3 Proof of the third Bieberbach Theorem; 2.4 Exercises; 3. Classification Methods; 3.1 Three methods of classification; 3.1.1 The methods of Calabi and Auslander-Vasquez; 3.2 Classification in dimension two; 3.3 Platycosms; 3.4 Exercises; 4. Flat Manifolds with b1 = 0; 4.1 Examples of (non)primitive groups; 4.2 Minimal dimension; 4.3 Exercises; 5. Outer Automorphism Groups 327 $a5.1 Some representation theory and 9-diagrams5.2 Infinity of outer automorphism group; 5.3 R1 - groups; 5.4 Exercises; 6. Spin Structures and Dirac Operator; 6.1 Spin(n) group; 6.2 Vector bundles; 6.3 Spin structure; 6.3.1 Case of cyclic holonomy; 6.4 The Dirac operator; 6.5 Exercises; 7. Flat Manifolds with Complex Structures; 7.1 Kahler flat manifolds in low dimensions; 7.2 The Hodge diamond for Kahler flat manifolds; 7.3 Exercises; 8. Crystallographic Groups as Isometries of Hn; 8.1 Hyperbolic space Hn; 8.2 Exercises; 9. Hantzsche-Wendt Groups; 9.1 Definitions; 9.2 Non-oriented GHW groups 327 $a9.3 Graph connecting GHW manifolds9.4 Abelianization of HW group; 9.5 Relation with Fibonacci groups; 9.6 An invariant of GHW; 9.7 Complex Hantzsche-Wendt manifolds; 9.8 Exercises; 10. Open Problems; 10.1 The classification problems; 10.2 The Anosov relation for flat manifolds; 10.3 Generalized Hantzsche-Wendt flat manifolds; 10.4 Flat manifolds and other geometries; 10.5 The Auslander conjecture; Appendix A Alternative Proof of Bieberbach Theorem; Appendix B Burnside Transfer Theorem; Appendix C Example of a Flat Manifold without Symmetry; Bibliography; Index 330 $aCrystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. They got their name, because in three dimensions they occur as the symmetry groups of a crystal (which we imagine to extend to infinity in all directions). The book is divided into two parts. In the first part, the basic theory of crystallographic groups is developed from the very beginning, while in the second part, more advanced and more recent topics are discussed. So the first part of the book should be usable as a textbook, while the second part is more interesting to resea 410 0$aALGEBRA AND DISCRETE MATHEMATICS 606 $aSymmetry groups 606 $aCrystallography, Mathematical 615 0$aSymmetry groups. 615 0$aCrystallography, Mathematical. 676 $a548/.81 700 $aSzczepan?ski$b Andrzej$01534672 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910785918503321 996 $aGeometry of crystallographic groups$93782418 997 $aUNINA