Geometric topology | Surgery theory | Algebraic K-theory
In geometric topology, a field within mathematics, the obstruction to a finitely dominated space X being homotopy-equivalent to a finite CW-complex is its Wall finiteness obstruction w(X) which is an element in the reduced zeroth algebraic K-theory of the integral group ring . It is named after the mathematician C. T. C. Wall. By work of John Milnor on finitely dominated spaces, no generality is lost in letting X be a CW-complex. A finite domination of X is a finite CW-complex K together with maps and such that . By a construction due to Milnor it is possible to extend r to a homotopy equivalence where is a CW-complex obtained from K by attaching cells to kill the relative homotopy groups . The space will be finite if all relative homotopy groups are finitely generated. Wall showed that this will be the case if and only if his finiteness obstruction vanishes. More precisely, using covering space theory and the Hurewicz theorem one can identify with . Wall then showed that the cellular chain complex is chain-homotopy equivalent to a chain complex of finite type of projective -modules, and that will be finitely generated if and only if these modules are stably-free. Stably-free modules vanish in reduced K-theory. This motivates the definition . (Wikipedia).
Computing Limits from a Graph with Infinities
In this video I do an example of computing limits from a graph with infinities.
From playlist Limits
Calculus I - 3.5.1 Limits at Infinity
In this video, we will explore the limit that our function approaches as the x-value gets increasingly large or increasingly small. For some functions, that limit will be a finite value. For others, the limit will be at infinity. ** Note - the computational strategies will be covered in vi
From playlist Calculus I - Complete Course Under Construction
Every Subset of the Discrete Topology has No Limit Points Proof
Every Subset of the Discrete Topology has No Limit Points Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
Limit doesn't exist 2 variables example
Example of how to show a limit doesn't exist for a function of 2 variables.
From playlist Engineering Mathematics
Part 1: Formal Definition of a Limit
This video states the formal definition of a limit and provide an epsilon delta proof that a limit exists. complete Video Library at http://www.mathispower4u.com
From playlist Limits
Diophantine analysis in thin orbits - Alex Kontorovich
Special Seminar Topic: Diophantine analysis in thin orbits Speaker: Alex Kontorovich Affiliation: Rutgers University; von Neumann Fellow, School of Mathematics Date: December 8, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds - Mohan Swaminathan
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds Speaker: Mohan Swaminathan Affiliation: Princeton Date: June 25, 2021 I will describe my recent work, joint with Shaoyun Bai, which studies a
From playlist Mathematics
Arka Banerjee - Obstruction to Coarse Embedding
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Arka Banerjee, University of Wisconsin-Milwaukee Title: Obstruction to coarse embedding Abstract: Van Kampen developed an obstruction theory for embedding a finite n-complex K into Euclidean 2n-space. A modern approach to
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Cyril Demarche: Cohomological obstructions to local-global principles - lecture 3
Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these
From playlist Algebraic and Complex Geometry
Vaughn Climenhaga: Beyond Bowen specification property - lecture 2
Rufus Bowen introduced the specification property for uniformly hyperbolic dynamical systems and used it to establish uniqueness of equilibrium states, including the measure of maximal entropy. After reviewing Bowen's argument, we will present our recent work on extending Bowen's approach
From playlist Dynamical Systems and Ordinary Differential Equations
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 3/5
1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, cosection localisation and a vanishing theorem 4. Refined Vafa-Witten invariants
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
The limit is the limit is the limit is the limit
Here I evaluate a neat infinite limit with l'Hopital's rule... does it work though? Subscribe to my channel: https://youtube.com/drpeyam Check out my TikTok channel: https://www.tiktok.com/@drpeyam Follow me on Instagram: https://www.instagram.com/peyamstagram/ Follow me on Twitter: https
From playlist Calculus
In this video, we give an important motivation for studying Topological Cyclic Homology, so called "trace methods". 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://w
From playlist Topological Cyclic Homology
Non-displaceable Lagrangian links in four-manifolds - Cheuk Yu Mak
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Non-displaceable Lagrangian links in four-manifolds Speaker: Cheuk Yu Mak Affiliation: University of Edinburgh Date: February 12, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Noncommutative Geometric Invariant Theory (Lecture 4) by Arvid Siqveland
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
The most difficult topic in limits: the indeterminate form.
From playlist Life Science Math: Limits in calculus
This video covers the laws of limits and how we use them to evaluate a limit. These laws are especially handy for continuous functions. More theorems about limits are introduced in later videos. For more videos visit http://www.mysecretmathtutor.com
From playlist Calculus
Richard Thomas - Vafa-Witten Invariants of Projective Surfaces 5/5
This course has 4 sections split over 5 lectures. The first section will be the longest, and hopefully useful for the other courses. 1. Sheaves, moduli and virtual cycles 2. Vafa-Witten invariants: stable and semistable cases 3. Techniques for calculation --- virtual degeneracy loci, cose
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory