In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold. For example in knot theory, one considers two knots the same if one can distort one knot into the other without breaking it. Such a distortion is an example of an ambient isotopy. More precisely, let and be manifolds and and be embeddings of in . A continuous map is defined to be an ambient isotopy taking to if is the identity map, each map is a homeomorphism from to itself, and . This implies that the orientation must be preserved by ambient isotopies. For example, two knots that are mirror images of each other are, in general, not equivalent. (Wikipedia).
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
This geometry video tutorial provides a basic introduction into isosceles trapezoids. It discusses the basic properties of isosceles trapezoids. The bases are parallel and the legs are congruent. The lower base angles are congruent and the upper base angles are congruent. The lower bas
From playlist Geometry Video Playlist
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
From playlist Geometry: Dynamic Interactives!
Andreas Zastrow: An Embedded Circle into R3 Might Escape Before an Isotoped Linked Circle
Andreas Zastrow, University of Gdansk (Inst. Math.) Title: An Embedded Circle into R3 Might Not Be Able to Escape Before an Isotoped Linked Circle The mathematically precise statement of the problem that was intuitively described in the title is following isotopy-extension problem: Given t
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
What is an equilateral triangle
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Max Zahoransky von Worlik: The Alexander Polynomial for Knots in the 3-Torus
Max Zahoransky von Worlik, Technische Universitat Berlin Title: The Alexander Polynomial for Knots in the 3-Torus In this talk I will explain how to obtain diagrammatic representations for knots and links in the 3-torus. This includes a discussion of how one can obtain a complete set of is
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
A Tour of Skein Modules by Rhea Palak Bakshi
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Hannah Schwartz - The presence of 2-torsion
June 21, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry Two knots in S^3 are ambiently isotopic if and only if there is an orientation preserving automorphism of S^3 carrying one knot to the other (this foll
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry I
Zack Sylvan - Doubling stops & spherical swaps
June 28, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry
From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry II
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Mathematical Magic: Unlinking a Pair of Handcuffs
Suppose you have a pair of handcuffs linked together. Can you pull them apart without unlocking them, breaking them, or letting them pass through themselves? With real handcuffs, definitely not! But for handcuffs made out of stretchy rubber, it turns out to be possible—as shown in this
From playlist Repulsive Videos
Mathematical Magic: Undoing Handcuffs
Suppose you have a pair of handcuffs locked to a post. Can you remove one of the cuffs without unlocking them, breaking them, or letting them pass through themselves? With real handcuffs, definitely not! But for handcuffs made out of stretchy rubber, it turns out to be possible—as shown
From playlist Repulsive Videos
Florian Frick (5/9/22): Chirality and quantifying embeddability
The combinatorics of triangulations of a space X provide upper bounds for the topology of the space of embeddings of X into d-dimensional Euclidean space. I will explain the previous sentence and as a consequence present generalizations of classical non-embeddability results. For example,
From playlist Bridging Applied and Quantitative Topology 2022
Legendrian and Transverse Knots by Dheeraj Kulkarni
DATE & TIME: 25 December 2017 to 04 January 2018 VENUE: Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex structure. The moduli space of these curves (
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
👉 Learn the essential definitions of triangles. A triangle is a polygon with three sides. Triangles are classified on the basis of their angles or on the basis of their side lengths. The classification of triangles on the bases of their angles are: acute, right and obtuse triangles. The cl
From playlist Types of Triangles and Their Properties
Erin Chambers (2/5/19): Computing optimal homotopies
Abstract: The question of how to measure similarity between curves in various settings has received much attention recently, motivated by applications in GIS data analysis, medical imaging, and computer graphics. Geometric measures such as Hausdorff and Fr\'echet distance have efficient al
From playlist AATRN 2019