Group actions (mathematics) | Generalized manifolds | Differential topology
In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space. Definitions of orbifold have been given several times: by Ichirô Satake in the context of automorphic forms in the 1950s under the name V-manifold; by William Thurston in the context of the geometry of 3-manifolds in the 1970s when he coined the name orbifold, after a vote by his students; and by André Haefliger in the 1980s in the context of Mikhail Gromov's programme on CAT(k) spaces under the name orbihedron. Historically, orbifolds arose first as surfaces with singular points long before they were formally defined. One of the first classical examples arose in the theory of modular forms with the action of the modular group on the upper half-plane: a version of the Riemann–Roch theorem holds after the quotient is compactified by the addition of two orbifold cusp points. In 3-manifold theory, the theory of Seifert fiber spaces, initiated by Herbert Seifert, can be phrased in terms of 2-dimensional orbifolds. In geometric group theory, post-Gromov, discrete groups have been studied in terms of the local curvature properties of orbihedra and their covering spaces. In string theory, the word "orbifold" has a slightly different meaning, discussed in detail below. In two-dimensional conformal field theory, it refers to the theory attached to the fixed point subalgebra of a vertex algebra under the action of a finite group of automorphisms. The main example of underlying space is a quotient space of a manifold under the properly discontinuous action of a possibly infinite group of diffeomorphisms with finite isotropy subgroups. In particular this applies to any action of a finite group; thus a manifold with boundary carries a natural orbifold structure, since it is the quotient of its double by an action of . One topological space can carry different orbifold structures. For example, consider the orbifold O associated with a quotient space of the 2-sphere along a rotation by ; it is homeomorphic to the 2-sphere, but the natural orbifold structure is different. It is possible to adopt most of the characteristics of manifolds to orbifolds and these characteristics are usually different from correspondent characteristics of underlying space. In the above example, the orbifold fundamental group of O is and its orbifold Euler characteristic is 1. (Wikipedia).
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: General Relativity
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Physics
Octahedron in Geogebra [Tutorial]
Octahedron in Geogebra [Tutorial] In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Octahedron in Geogebra Step by step tutorial here: https://youtu.be/LmCs6dzZreA In case you wanna to pay me a drink: https://www.paypal.me/admirsuljicic/
From playlist Geogebra [Tutoriali]
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Physics
GeoGebra Scientific Calculator: When to Use?
GeoGebra Scientific Calculator is a free easy-to-use version of a standard handled scientific calculator. https://www.geogebra.org/scientific
From playlist GeoGebra Apps Intro: Which to USE?
From playlist the absolute best of stereolab
The Weil-Petersson current for moduli of vector bundles and... by Schumacher
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Volume and Homology for Hyperbolic 3-Orbifolds...Arithmetic Groups - Peter Shalen
Peter Shalen December 1, 2015 https://www.math.ias.edu/seminars/abstract?event=83284 A theorem of Borel's asserts that for any positive real number V, there are at most finitely many arithmetic lattices in PSL2(ℂ) of covolume at most V, or equivalently at most finitely many arithmetic hy
From playlist Mathematics
J. Demailly - Existence of logarithmic and orbifold jet differentials
Abstract - Given a projective algebraic orbifold, one can define associated logarithmic and orbifold jet bundles. These bundles describe the algebraic differential operators that act on germs of curves satisfying ad hoc ramification conditions. Holomorphic Morse inequalities can be used to
From playlist Ecole d'été 2019 - Foliations and algebraic geometry
AdS3 at the String Scale by Matthias Gaberdiel
ORGANIZERS : Pallab Basu, Avinash Dhar, Rajesh Gopakumar, R. Loganayagam, Gautam Mandal, Shiraz Minwalla, Suvrat Raju, Sandip Trivedi and Spenta Wadia DATE : 21 May 2018 to 02 June 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore In the past twenty years, the discovery of the AdS/C
From playlist AdS/CFT at 20 and Beyond
Algebraic geometry 45: Hurwitz curves
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It discusses Hurwitz curves and sketches a proof of Hurwitz's bound for the symmetry group of a complex curve.
From playlist Algebraic geometry I: Varieties
Four Color Theorem via Gauge Theory and Three Manifold Topology - Tom Mrowka [2016]
slides for this talk: https://drive.google.com/file/d/1o-WQOW5Dwec5AmMNelfaJAu4KxOS4vdm/view?usp=sharing Name: Tom Mrowka Event: Workshop: Recent Developments in the Mathematical study of Gauge Theory Event URL: view webpage Title: An approach to the Four Color Theorem via Gauge Theory an
From playlist Mathematics
Conebranes Igor Klebanov Princeton University July 26, 2010
From playlist PiTP 2010
Alessandro Chiodo - Towards a global mirror symmetry (Part 1)
Mirror symmetry is a phenomenon which inspired fundamental progress in a wide range of disciplines in mathematics and physics in the last twenty years; we will review here a number of results going from the enumerative geometry of curves to homological algebra. These advances justify the i
From playlist École d’été 2011 - Modules de courbes et théorie de Gromov-Witten
Open-Closed Gromov-Witten Invariants of Toric Calabi-Yau 3-Orbifolds - Chiu-Chu Melissa Liu
Chiu-Chu Melissa Liu Columbia University December 7, 2012 We study open-closed orbifold Gromov-Witten invariants of toric Calabi-Yau 3-orbifolds with respect to Lagrangian branes of Aganagic-Vafa type. We prove an open mirror theorem which expresses generating functions of orbifold disk in
From playlist Mathematics
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Physics
Birational Geometry and Orbifold Pairs : Arithmetic and hyperbolic (Lecture 5) by Frederic Campana
PROGRAM : TOPICS IN BIRATIONAL GEOMETRY ORGANIZERS : Indranil Biswas and Mahan Mj DATE : 27 January 2020 to 31 January 2020 VENUE : Madhava Lecture Hall, ICTS Bangalore Birational geometry is one of the current research trends in fields of Algebraic Geometry and Analytic Geometry. It ca
From playlist Topics In Birational Geometry