Surgery theory | Differential topology | Algebraic topology
In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same dimension are cobordant if their disjoint union is the boundary of a compact manifold one dimension higher. The boundary of an (n + 1)-dimensional manifold W is an n-dimensional manifold ∂W that is closed, i.e., with empty boundary. In general, a closed manifold need not be a boundary: cobordism theory is the study of the difference between all closed manifolds and those that are boundaries. The theory was originally developed by René Thom for smooth manifolds (i.e., differentiable), but there are now also versions forpiecewise linear and topological manifolds. A cobordism between manifolds M and N is a compact manifold W whose boundary is the disjoint union of M and N, . Cobordisms are studied both for the equivalence relation that they generate, and as objects in their own right. Cobordism is a much coarser equivalence relation than diffeomorphism or homeomorphism of manifolds, and is significantly easier to study and compute. It is not possible to classify manifolds up to diffeomorphism or homeomorphism in dimensions ≥ 4 – because the word problem for groups cannot be solved – but it is possible to classify manifolds up to cobordism. Cobordisms are central objects of study in geometric topology and algebraic topology. In geometric topology, cobordisms are with Morse theory, and h-cobordisms are fundamental in the study of high-dimensional manifolds, namely surgery theory. In algebraic topology, cobordism theories are fundamental extraordinary cohomology theories, and categories of cobordisms are the domains of topological quantum field theories. (Wikipedia).
Trigonometry 5 The Cosine Relationship
A geometrical explanation of the law of cosines.
From playlist Trigonometry
Covariance (1 of 17) What is Covariance? in Relation to Variance and Correlation
Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
Lagrangian cobordism: what we know and what is it good for - Octav Cornea
Octav Cornea University of Montreal October 2, 2015 http://www.math.ias.edu/calendar/event/85014/1443808800/1443812400 I will describe how the notion of Lagrangian cobordism, introduced by Arnold in 1980, offers a systematic perspective on the study of Lagrangian topology. There are thre
From playlist Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Applying the law of cosines to solve a word problem
Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th
From playlist Solve Law of Cosines (Word Problem) #ObliqueTriangles
What is a Coulomb? An Explanation
Gives a comprehensive description of what coulomb is. Includes three worked examples; how to calculate the number of electrons in a coulomb, number of electrons in a given amount of charge and charge from a given number of electrons. You can see a listing of all my videos at my website,
From playlist Electricity and Magnetism
Chris Stewart (Pt. 1) - Aesthetic Cognitivism: Overview & Concepts
Free access to Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Aesthetic Cognitivism is a theory about the value of the arts as sources of understanding—the arts as more than sources of delight, amusement, pleasure, or emotional catharsis (though they can certainly be all
From playlist Aesthetic Cognitivism: Overview & Concepts - CTT Interview Series
Trigonometry 7 The Cosine of the Sum and Difference of Two Angles
A geometric proof of the cosine of the sum and difference of two angles identity.
From playlist Trigonometry
Paul BIRAN - Lagrangian Cobordisms, Dehn-twists and Real Algebraic Geometry
We will explain the relevance of Lagrangian cobordisms in Lefschetz fibrations to the study of the (derived) Fukaya category of the fiber. In particular we will give a cobordism interpretation of Seidel's long exact sequence, introduce cobordism groups and also outline how to study real al
From playlist 2015 Summer School on Moduli Problems in Symplectic Geometry
A quantitative look at Lagrangian cobordisms - Lisa Traynor
Augmentations and Legendrians at the IAS Topic: A quantitative look at Lagrangian cobordisms Speaker: Lisa Traynor Date: Friday, February 12 Lagrangian cobordisms between Legendrian submanifolds arise in Relative Symplectic Field Theory. In recent years, there has been much progress on an
From playlist Mathematics
Applying the law of cosines when given SAS
Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th
From playlist Law of Cosines
Restrictions on the fundamental group of some Lagrangian cobordisms - Chantraine
Restrictions on the fundamental group of some Lagrangian cobordisms Augmentations and Legendrians at the IAS Topic: Restrictions on the fundamental group of some Lagrangian cobordisms Speaker: Baptiste Chantraine Date: Thursday, February 11 In this talk we will describe two methods which
From playlist Mathematics
Using the law of cosines for a triangle with SAS
Learn how to solve for the lengths of the sides and the measures of the angles of a triangle using the law of cosines. The law of cosines is used in determining the lengths of the sides or the measures of the angles of a triangle when no angle measure and the length of the side opposite th
From playlist Law of Cosines
Yonatan Harpaz - New perspectives in hermitian K-theory II
Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory
On the Lagrangian cobordism relation on Legendrian links -Joshua Sabloff
Seminar in Analysis and Geometry Topic: On the Lagrangian cobordism relation on Legendrian links Speaker: Joshua Sabloff Affiliation: Member, School of Mathematics Date: February 22, 2022 Lagrangian cobordism induces a preorder on the set of Legendrian links in any contact 3-manifold. We
From playlist Mathematics
Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants - Ipsita Datta
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants Speaker: Ipsita Datta Affiliation: Member, School of Mathematics Date: November 4, 2022 We introduce new invariants to the existence of
From playlist Mathematics
The homology cobordism group - Linh Truong
Short talks by postdoctoral members Topic: The homology cobordism group Speaker: Linh Truong Affiliation: Member, School of Mathematics Date: September 27, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics
Lagrangian Cobordisms and Enriched Knot Diagrams - Ipsita Datta
Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Lagrangian Cobordisms and Enriched Knot Diagrams Speaker: Ipsita Datta Affiliation: Member, School of Mathematics Date: November 08, 2021 We present some obstructions to the existence of Lagrangian cobordisms in ℝ4. The ob
From playlist Mathematics
Trigonometry 9 The Sum of Cosines.mov
The sum of the cosine of two angles.
From playlist Trigonometry
Classifying (quasi-)smooth varieties up to cobordism - Toni Mikael Annala
Short Talks by Postdoctoral Members Topic: Classifying (quasi-)smooth varieties up to cobordism Speaker: Toni Mikael Annala Affiliation: Member, School of Mathematics Date: September 20, 2022
From playlist Mathematics