Geometric topology | General topology | Homeomorphisms
In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the static homeomorphism: The result is a fiber bundle whose base is a circle and whose fiber is the original space X. If X is a manifold, Mf will be a manifold of dimension one higher, and it is said to "fiber over the circle". As a simple example, let be the circle, and be the inversion , then the mapping torus is the Klein bottle. Mapping tori of surface homeomorphisms play a key role in the theory of 3-manifolds and have been intensely studied. If S is a closed surface of genus g ≥ 2 and if f is a self-homeomorphism of S, the mapping torus Mf is a closed 3-manifold that fibers over the circle with fiber S. A deep result of Thurston states that in this case the 3-manifold Mf is hyperbolic if and only if f is a pseudo-Anosov homeomorphism of S. (Wikipedia).
Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with many rings,and transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2014,AkiraNishihara
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Parametric torus from parameter space
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Spherical Earth: https://skfb.ly/NNrH Torus Earth: https://skfb.ly/MYpC Shapeways link: http://shpws.me/M9NI Joint work with Saul Schleimer.
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360-Degree Tour INSIDE a TORUS with GeoGebra Augmented Reality
Come take a virtual tour as we walk around INSIDE a closed torus! Also, come explore some lesson ideas with respect to using GeoGebra Augmented Reality to explore conic sections, form surfaces of revolutions (by rotating graphs about the x-axis & y-axis), and model in 3D! https://www.geoge
From playlist GeoGebra Augmented Reality (older iOS app)
Buy at http://www.shapeways.com/shops/GeometricToy Torus Magic is a transformable torus. This torus object is constructed with 20 large rings(50mm diameter) and many small rings.It transforms flat,spherical etc. Also you can turn inside out the torus. Copyright (c) 2015,AkiraNishihara
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Morphing a Torus: Quick GeoGebra 3D Graphing Calculator with Augmented Reality Demo
Screencast recorded on iPadPro. GeoGebra 3D Graphing Calculator with Augmented Reality. Quick Link: https://www.geogebra.org/m/h2fkfsfm
From playlist GeoGebra 3D with AR (iOS): Explorations, Demos, and Lesson Ideas
Buy at http://www.shapeways.com/shops/GeometricToy "Torus Magic" can eat another torus.This torus object is constructed with 30 large rings(70mm diameter) and many small rings. Copyright (c) 2015,AkiraNishihara
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Nonlinear algebra, Lecture 7: "Toric Varieties", by Mateusz Michalek
This is the seventh lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
A Continuous Transformation of a Double Cover of the Complex Plane into a Torus
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Dominic Milioto Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, a
From playlist Wolfram Technology Conference 2017
Nonlinear algebra, Lecture 9: "Representation Theory", by Mateusz Michalek
This is the ninth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Symplectic Dynamics of Integrable Hamiltonian Systems - Alvaro Pelayo
Alvaro Pelayo Member, School of Mathematics April 4, 2011 I will start with a review the basic notions of Hamiltonian/symplectic vector field and of Hamiltonian/symplectic group action, and the classical structure theorems of Kostant, Atiyah, Guillemin-Sternberg and Delzant on Hamiltonian
From playlist Mathematics
Random walks on Tori and normal numbers in self similar sets by Arijit Ganguly
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Entropy, Algebraic Integers and Moduli of Surfaces - Curtis McMullen
Curtis McMullen Harvard University December 7, 2010 For more videos, visit http://video.ias.edu
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Mirror symmetry and cluster algebras – Paul Hacking & Sean Keel – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.15 Mirror symmetry and cluster algebras Paul Hacking & Sean Keel Abstract: We explain our proof, joint with Mark Gross and Maxim Kontsevich, of conjectures of Fomin–Zelevinsky and Fock–Goncharov on canonical bases of cluster algebras. We i
From playlist Algebraic & Complex Geometry
Dimers and Beauville Integrable systems by Terrence George
PROGRAM: COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
Lagrangians, symplectomorphisms and zeroes of moment maps - Yann Rollin
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Lagrangians, symplectomorphisms and zeroes of moment maps Speaker: Yann Rollin Affiliation: Nantes University Date: April 08, 2022 I will present two constructions of Kähler manifolds, endowed with Hamiltonia
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STPM - New Tools for an Old Problem: The Dynamics of Area Preserving Disc Maps - Braney Bramham
Braney Bramham Institute for Advanced Study September 21, 2010 For more videos, visit http://video.ias.edu
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