Spectral sequences | Homotopy theory

In mathematics, the Adams spectral sequence is a spectral sequence introduced by J. Frank Adams which computes the stable homotopy groups of topological spaces. Like all spectral sequences, it is a computational tool; it relates homology theory to what is now called stable homotopy theory. It is a reformulation using homological algebra, and an extension, of a technique called 'killing homotopy groups' applied by the French school of Henri Cartan and Jean-Pierre Serre. (Wikipedia).

Spectral Sequences 02: Spectral Sequence of a Filtered Complex

I like Ivan Mirovic's Course notes. http://people.math.umass.edu/~mirkovic/A.COURSE.notes/3.HomologicalAlgebra/HA/2.Spring06/C.pdf Also, Ravi Vakil's Foundations of Algebraic Geometry and the Stacks Project do this well as well.

From playlist Spectral Sequences

What is the alternate in sign sequence

đź‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

What is the definition of a geometric sequence

đź‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

Stable Homotopy Seminar, 19: The Adams spectral sequence (D. Zack Garza)

This talk by D. Zack Garza is all about the Adams spectral sequence, which is a powerful tool for computing homotopy classes of maps of spectra in terms of their cohomology for some cohomology theory E. The spectral sequence looks like: Ext_{E^*}(E^*Y, E^*X) â‡’ (a completion of) [X, Y]. We'

From playlist Stable Homotopy Seminar

What is an arithmetic sequence

đź‘‰ Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which

From playlist Sequences

What is the definition of an arithmetic sequence

From playlist Sequences

Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/4N5kk6MNT5DMqfp I will discuss a program for computing C2-equivariant, â„ť-motivic, â„‚-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Daniel Isaksen - 1/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/F2BoSJ7zgfipRxP I will discuss a program for computing C2-equivariant, â„ť-motivic, â„‚-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Chapter 5 - Geometric Sequences - IB Math Studies (Math SL)

Hello and welcome to What Da Math This video is an introduction to sequences and series and is meant to explain what this topic is about in layman's terms. This video focuses on geometric sequences. This is from Chapter 5 Haese edition of IB Math Studies book. SUBSCRIBE for more math an

From playlist IB Math Studies Chapter 5

Stable Homotopy Seminar, 20: Computations with the Adams Spectral Sequence (Jacob Hegna)

Jacob Hegna walks us through some of the methods which have been used to compute the E_2 page of the Adams spectral sequence for the sphere, a.k.a. Ext_A(F_2, F_2), where A is the Steenrod algebra. The May spectral sequence works by filtering A and first computing Ext over the associated g

From playlist Stable Homotopy Seminar

Jeremy Hahn : Prismatic and syntomic cohomology of ring spectra

CONFERENCE Recording during the thematic meeting : Â« Chromatic Homotopy, K-Theory and FunctorsÂ» the January 24, 2023 at the Centre International de Rencontres MathĂ©matiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR

From playlist Topology

How to write the explicit formula for a geometric sequence given the 10th term and ratio

đź‘‰ Learn how to write the explicit formula for a geometric sequence. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. A geometric sequence is a sequence in which each term of the sequence is obtained by multi

From playlist Sequences

Stable Homotopy Seminar, 16: The Whitehead, Hurewicz, Universal Coefficient, and KĂĽnneth Theorems

These are some generalizations of facts from unstable algebraic topology that are useful for calculating in the category of spectra. The Whitehead and Hurewicz theorems say that a map of connective spectra that's a homology isomorphism is a weak equivalence, and that the lowest nonzero hom

From playlist Stable Homotopy Seminar

Stable Homotopy Seminar, 17: Universal Coefficient Theorem, Moore Spectra, and Limits

We finish constructing the universal coefficient spectral sequence, and look at some classical examples involving Moore spectra. As it turns out, it's really easy in stable homotopy theory to invert or localize at a prime. In particular, *rational* stable homotopy theory is completely alge

From playlist Stable Homotopy Seminar

What is the difference between finite and infinite sequences

From playlist Sequences

Calculations in the stable homotopy categories - Hana Jia Kong

Short Talks by Postdoctoral Members Topic: Calculations in the stable homotopy categories Speaker: Hana Jia Kong Affiliation: Member, School of Mathematics Date: September 28, 2022

From playlist Mathematics

Teena Gerhardt - 3/3 Algebraic K-theory and Trace Methods

Algebraic K-theory is an invariant of rings and ring spectra which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approac

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory