Homotopy theory | Lorentzian manifolds | Algebraic topology

Timelike homotopy

On a Lorentzian manifold, certain curves are distinguished as timelike. A timelike homotopy between two timelike curves is a homotopy such that each intermediate curve is timelike. No closed timelike curve (CTC) on a Lorentzian manifold is timelike homotopic to a point (that is, null timelike homotopic); such a manifold is therefore said to be multiply connected by timelike curves (or timelike multiply connected). A manifold such as the 3-sphere can be simply connected (by any type of curve), and at the same time be timelike multiply connected. Equivalence classes of timelike homotopic curves define their own fundamental group, as noted by Smith (1967). A smooth topological feature which prevents a CTC from being deformed to a point may be called a timelike topological feature. (Wikipedia).

Video thumbnail

Homomorphisms in abstract algebra

In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu

From playlist Abstract algebra

Video thumbnail

Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine

(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des

From playlist Mathematics

Video thumbnail

Homotopy animation

An interesting homotopy (in fact, an ambient isotopy) of two surfaces.

From playlist Algebraic Topology

Video thumbnail

Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS

The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t

From playlist Introduction to Homotopy Theory

Video thumbnail

Homotopy type theory: working invariantly in homotopy theory -Guillaume Brunerie

Short talks by postdoctoral members Topic: Homotopy type theory: working invariantly in homotopy theory Speaker: Guillaume Brunerie Affiliation: Member, School of Mathematics Date: September 26, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Wolfram Physics Project: Working Session Friday, Apr. 17, 2020 [Spin & Charge | Part 1]

Stephen Wolfram & Jonathan Gorard & Max Piskunov continue answering questions about the new Wolfram Physics Project, this time specifically for the first live working session of the project. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by

From playlist Wolfram Physics Project Livestream Archive

Video thumbnail

Introduction to Homotopy Theory- Part 5- Transition to Abstract Homotopy Theory

Credits: nLab: https://ncatlab.org/nlab/show/Introdu...​ Animation library: https://github.com/3b1b/manim​​​ Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bit.ly/31Ma5s0​​​ • Spotify Track Link: https://spoti.fi/

From playlist Introduction to Homotopy Theory

Video thumbnail

Wolfram Physics Project: Working Session Monday, Apr. 20, 2020 [Spin & Charge | Part 2]

Stephen Wolfram & Jonathan continue answering questions about the new Wolfram Physics Project, this time for a continuation of the first live working session, we'll be continuing our discussion on spin and charge. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-

From playlist Wolfram Physics Project Livestream Archive

Video thumbnail

Scott Aaronson - Complexity and computability with closed timelike curves [2018]

Scott Aaronson (02/23/18) https://media.ma.utexas.edu/media/Math_Club/Scott_Aaronson/

From playlist Mathematics

Video thumbnail

Invariant homotopy theory in the univalent foundations - Guillaume Brunerie

Topic: Invariant homotopy theory in the univalent foundations Speaker: Guillaume Brunerie, Member, School of Mathematics Time/Room: 4:00pm - 4:15pm/S-101 More videos on http://video.ias.edu

From playlist Mathematics

Video thumbnail

Ken Olum - Is Time Travel Possible?

Free access Closer to Truth's library of 5,000 videos: http://bit.ly/2UufzC7 Some scientists take time travel seriously. Should you? What does time travel reveal about the nature of space and time? What about the laws of physics under extreme conditions? And don't forget those 'Grandfathe

From playlist Is Time Travel Possible? - CTT Interview Series

Video thumbnail

Tim Maudlin - Is Time Travel Possible?

Some scientists take time travel seriously. Should you? What does time travel reveal about the nature of space and time? What about the laws of physics under extreme conditions? And don't forget those 'Grandfather Paradoxes', where a time traveler kills his own ancestor. Click here to wat

From playlist Is Time Travel Possible? - CTT Interview Series

Video thumbnail

Causality & Light Cones | Special Relativity

▶ Topics ◀ Timelike, Spacelike Vectors, Causality, Light Cone, Past, Future ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support

From playlist Special Relativity, General Relativity

Video thumbnail

Is Time Travel Impossible?

PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateSPACE ↓ More info below ↓ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Check out the Space Time Merch Store https://pbsspacetim

From playlist Teach physics with fun! (video games, sci-fi, etc...)

Video thumbnail

Minimal surfaces in R^3 and Maximal surfaces in L^3 (Lecture 2) by Pradip Kumar

ORGANIZERS : C. S. Aravinda and Rukmini Dey DATE & TIME : 16 June 2018 to 25 June 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore This workshop on geometry and topology for lecturers is aimed for participants who are lecturers in universities/institutes and colleges in India. This w

From playlist Geometry and Topology for Lecturers

Video thumbnail

Can We Actually Time Travel? Einstein Says 'Ja!'

Episode 2 of 4 Check us out on Soundcloud! https://soundcloud.com/dnewsplus Please Subscribe! http://bit.ly/28iQhYC Check out http://www.evemattress.com and enter "plus125" to get $125 off today! "Next generation memory foam is layered with a patented comfort layer which gives

From playlist Have We Already Time Traveled?

Video thumbnail

James Stasheff (8/31/22): Homotopy coherence - theme and variations

This survey will be semi-historical and idiosyncratic with the topics covered determined by the knowledge and taste of the authors, but we hope it will provide some links that may not be common knowledge between the various aspects of the theory of homotopy coherence and, in particular, to

From playlist AATRN 2022

Video thumbnail

Computing homology groups | Algebraic Topology | NJ Wildberger

The definition of the homology groups H_n(X) of a space X, say a simplicial complex, is quite abstract: we consider the complex of abelian groups generated by vertices, edges, 2-dim faces etc, then define boundary maps between them, then take the quotient of kernels mod boundaries at each

From playlist Algebraic Topology

Video thumbnail

Sergiu Klainerman - 1/4 On the Mathematical Theory of Black Holes

https://indico.math.cnrs.fr/event/3463/ The gravitational waves detected by LIGO were produced in the final faze of the inward spiraling of two black holes before they collided to produce a more massive black hole. The experiment is entirely consistent with the so called Final State Conjec

From playlist Sergiu Klainerman - On the Mathematical Theory of Black Holes

Video thumbnail

Homophily Solution - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Related pages

3-sphere | Closed timelike curve | Homotopy