Orbifold

Matematikaning topology va geometry sohalarida orbifold („orbit-manifold“, yaʼni orbitali koʻpxillik) manifoldning umumlashmasidir.

Manbalar

• Adem, Alejandro; Leida, Johann; Ruan, Yongbin. Orbifolds and Stringy Topology, Cambridge Tracts in Mathematics. Cambridge University Press, 2007. DOI:10.1017/CBO9780511543081. ISBN 978-0-521-87004-7. 
• Ballmann, Werner „Singular spaces of non-positive curvature“, . Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics. Birkhäuser, 1990 — 189–201-bet. ISBN 0-8176-3508-4. 
• Ballmann, Werner; Brin, Michael (1994). "Polygonal complexes and combinatorial group theory". Geometriae Dedicata 50 (2): 165–191. doi:10.1007/BF01265309. 
• Boileau, Michel „Geometrizations of 3-manifolds with symmetries“. 2011-yil 30-sentyabrda asl nusxadan arxivlangan. Qaraldi: 2007-yil 6-dekabr.
• Boileau, Michel; Maillot, Sylvain; Porti, Joan. Three-dimensional orbifolds and their geometric structures, Panoramas and Syntheses. Société Mathématique de France, 2003. ISBN 2-85629-152-X. OCLC 56349823. .
• Boileau, Michel; Leeb, Bernhard; Porti, Joan (2005). "Geometrization of 3-dimensional orbifolds". Annals of Mathematics 162: 195–290. doi:10.4007/annals.2005.162.195. 
• Bredon, Glen. Introduction to Compact Transformation Groups. Academic Press, 1972. ISBN 0-12-128850-1. 
• Bridson, Martin; Haefliger, André. Metric Spaces of Non-Positive Curvature, Grundlehren der mathematischen Wissenschaften. Springer, 1999. DOI:10.1007/978-3-662-12494-9. ISBN 3-540-64324-9. 
• Brin, Matthew (2007). "Seifert Fibered Spaces: Notes for a course given in the Spring of 1993". arXiv:0711.1346 [math.GT]. 
• Callender, Clifton; Quinn, Ian; Tymoczko, Dmitri (18 April 2008). "Generalized Voice-Leading Spaces". Science 320 (5874): 346–348. doi:10.1126/science.1153021. PMID 18420928. http://www.music.princeton.edu/~dmitri/voiceleading.pdf. Qaraldi: 24 January 2010. Orbifold]]
• Cartwright, Donald; Mantero, Anna Maria; Steger, Tim; Zappa, Anna (1993). "Groups acting simply transitively on the vertices of a building of type Ã₂, I". Geometriae Dedicata 47 (2): 143–166. doi:10.1007/BF01266617. 
• Cooper, Daryl; Hodgson, Craig; Kerckhoff, Steven. Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs. Mathematical Society of Japan, 2000. ISBN 4-931469-05-1. .
• de la Harpe, Pierre (1991). "An invitation to Coxeter group". Group theory from a geometrical viewpoint, 26 March - 6 April 1990, ICPT, Trieste, Italy (proceedings). Singapore: World Scientific. pp. 193–253. doi:10.1142/1235. ISBN 981-02-0442-6. .
• Di Francesco, Philippe; Mathieu, Pierre; Sénéchal, David. Conformal field theory, Graduate Texts in Contemporary Physics. Springer-Verlag, 1997. DOI:10.1007/978-1-4612-2256-9. ISBN 0-387-94785-X. .

• Haefliger, André. Groupoides d'holonomie et classifiants, Astérisque. Société Mathématique de France, 1984 — 70–97-bet. 
• Haefliger, André „Orbi-espaces“, . Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics. Birkhäuser, 1990 — 203–213-bet. DOI:10.1007/978-1-4684-9167-8_11. ISBN 0-8176-3508-4. 
• Haefliger, André (1991). "Complexes of groups and orbihedra". Group theory from a geometrical viewpoint, 26 March - 6 April 1990, ICPT, Trieste, Italy (proceedings). Singapore: World Scientific. pp. 504–540. doi:10.1142/1235. ISBN 981-02-0442-6. 
• Iglesias, Patrick; Karshon, Yael; Zadka, Moshe (June 2010). "Orbifolds as Diffeologies". Transactions of the American Mathematical Society 362 (6): 2811–2831. doi:10.1090/S0002-9947-10-05006-3. 
• Iglesias-Zemmour, Patrick. Diffeology, Mathematical Surveys and Monographs. American Mathematical Society, 2013. ISBN 978-0-8218-9131-5. 
• Iglesias-Zemmour, Patrick; Laffineur, Jean-Pierre (2017). "Noncommutative Geometry & Diffeology: The Case Of Orbifolds". Journal of Noncommutative Geometry 12 (4): 1551–1572. doi:10.4171/JNCG/319. 
• Kawakubo, Katsuo. The Theory of Transformation Groups. Oxford University Press, 1991. ISBN 0-19-853212-1. 
• Köhler, Peter; Meixner, Thomas; Wester, Michael (1985). "The 2-adic affine building of type Ã₂ and its finite projections". Journal of Combinatorial Theory. Series A 38 (2): 203–209. doi:10.1016/0097-3165(85)90070-6. 
• Mumford, David (1979). "An algebraic surface with K ample, (K²) = 9, p_g = q = 0". American Journal of Mathematics 101 (1): 233–244. doi:10.2307/2373947. http://nrs.harvard.edu/urn-3:HUL.InstRepos:3612860. 
• Poincaré, Henri. Papers on Fuchsian functions. Springer, 1985. ISBN 3-540-96215-8. 
• Satake, Ichirô (1956). "On a generalization of the notion of manifold". Proceedings of the National Academy of Sciences of the United States of America 42 (6): 359–363. doi:10.1073/pnas.42.6.359. PMID 16578464. PMC 528292. //www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=528292. 
• Satake, Ichirô (1957). "The Gauss-Bonnet theorem for V-manifolds". Journal of the Mathematical Society of Japan 9 (4): 464–492. doi:10.2969/jmsj/00940464. 
• Scott, Peter (1983). "The geometries of 3-manifolds". Bulletin of the London Mathematical Society 15 (5): 401–487. doi:10.1112/blms/15.5.401. http://www.math.lsa.umich.edu/~pscott/8geoms.pdf. 
  Errata: Scott, Peter „Errata for "The geometries of 3-manifolds", Bull. London Math. Soc. 15 (1983), 401-487“.
• Serre, Jean-Pierre. Cours d'arithmétique. Presse Universitaire de France, 1970. 
• Serre, Jean-Pierre. Trees. Springer, 2003. DOI:10.1007/978-3-642-61856-7. ISBN 978-3-642-61858-1. 
  Inglizcha tarjimasi: Serre, Jean-Pierre. Arbres, amalgames, SL₂, 3rd, Astérisque, Société Mathématique de France, 1983. 
• Stallings, John (1991). "Triangles of groups". Group theory from a geometrical viewpoint, 26 March - 6 April 1990, ICPT, Trieste, Italy (proceedings). Singapore: World Scientific. pp. 491–503. doi:10.1142/1235. ISBN 981-02-0442-6. 
• Świątkowski, Jacek (2001). "A class of automorphism groups of polygonal complexes". Quarterly Journal of Mathematics 52 (2): 231–247. doi:10.1093/qjmath/52.2.231. 
• Thurston, William. The Geometry and Topology of Three-Manifolds, Princeton University lecture notes, 1978–1981. 
• Thurston, William (1982). "Three-dimensional manifolds, Kleinian groups and hyperbolic geometry". Bulletin of the American Mathematical Society 6 (3): 357–381. doi:10.1090/S0273-0979-1982-15003-0. 
• Tymoczko, Dmitri (7 July 2006). "The Geometry of Musical Chords". Science 313 (5783): 72–74. doi:10.1126/science.1126287. PMID 16825563. http://www.brainmusic.org/EducationalActivitiesFolder/Tymoczko_chords2006.pdf.