In algebraic topology, a branch of mathematics, the (singular) homology of a topological space relative to a subspace is a construction in singular homology, for pairs of spaces. The relative homology is useful and important in several ways. Intuitively, it helps determine what part of an absolute homology group comes from which subspace. (Wikipedia).
Algebraic Topology - 11.3 - Homotopy Equivalence
We sketch why that the homotopy category is a category.
From playlist Algebraic Topology
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
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
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
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
This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios
Lecture 14: The Definition of TC
In this video, we finally give the definition of topological cyclic homology. In fact, we will give two definitions: the first is abstract in terms of a mapping spectrum spectrum in cyclotomic spectra and then we unfold this to a concrete definition on terms of negative topological cyclic
From playlist Topological Cyclic Homology
Group Homomorphisms - Abstract Algebra
A group homomorphism is a function between two groups that identifies similarities between them. This essential tool in abstract algebra lets you find two groups which are identical (but may not appear to be), only similar, or completely different from one another. Homomorphisms will be
From playlist Abstract Algebra
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Persistent matchmaking - Uli Bauer
Workshop on Topology: Identifying Order in Complex Systems Topic: Persistent matchmaking Speaker: Uli Bauer Affiliation: Technical University of Munich Date: March 5, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Lecture 4: The Connes operator on HH
Correction: The formula we give for the Connes operator B is slightly wrong, there needs to be a '+' instead of a '-' in between the two summands. In this video, we discuss the Connes operator on Hochschild homology. Feel free to post comments and questions at our public forum at https:
From playlist Topological Cyclic Homology
Vanessa Robins (9/8/22): The Extended Persistent Homology Transform for Manifolds with Boundary
The Persistent Homology Transform (PHT) is a topological transform introduced by Turner, Mukherjee and Boyer in 2014. Its input is a shape embedded in Euclidean space; then to each unit vector the transform assigns the persistence module of the height function over that shape with respect
From playlist AATRN 2022
Digression: Hochschild Homology of Schemes
We define and study Hochschild homology for schemes. This video is a slight digression from the rest of the lecture course and we assume familiarity with schemes. The exercise might be a bit tricky... Feel free to post comments and questions at our public forum at https://www.uni-muenste
From playlist Topological Cyclic Homology
Symplectic Instanton Homology of Knots and Links in 3-manifolds - David White
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Symplectic Instanton Homology of Knots and Links in 3-manifolds Speaker: David White Affiliation: North Carolina State University Date: February 10, 2023 Powerful homology invariants of knots in 3-manifolds
From playlist Mathematics
Sensors, sampling, and scale selection: a homological approach - Don Sheehy
Don Sheehy University of Connecticut April 18, 2015 In their seminal work on homological sensor networks, de Silva and Ghrist showed the surprising fact that its possible to certify the coverage of a coordinate free sensor network even with very minimal knowledge of the space to be covere
From playlist Mathematics
Birgit Richter: Juggling formulae for higher THH
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Topological Hochschild homology (THH) is the target of the trace map from algebraic K-theory. Similarly, iterated algebraic K-theory maps to an iterated version of THH, the so-called
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Versality for the relative Fukaya category - Nick Sheridan
Speaker: Nick Sheridan Title: Versality for the relative Fukaya category Affiliation: IAS Date: November 9, 2016 For more video, visit http://video.ias.edu
From playlist Mathematics
M. Pflaum: Localization in Hochschild homology and convolution algebras of circle actions
Talk by Shintaro Nishikawa in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on July 29, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Here we give a definition of the relative Frobenius. We also give a good notation that helps you forget about the annoying tensor product that nobody can remember.
From playlist Cartier Operator
Lecture 3: Classical Hochschild Homology
In this video, we introduce classical Hochschild homology and discuss the HKR theorem. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-muenster.de/IVV5WS/Web
From playlist Topological Cyclic Homology