In mathematics, a secondary cohomology operation is a functorial correspondence between cohomology groups. More precisely, it is a natural transformation from the kernel of some primary cohomology operation to the cokernel of another primary operation. They were introduced by J. Frank Adams in his solution to the Hopf invariant problem. Similarly one can define tertiary cohomology operations from the kernel to the cokernel of secondary operations, and continue like this to define higher cohomology operations, as in . Michael Atiyah pointed out in the 1960s that many of the classical applications could be proved more easily using generalized cohomology theories, such as in his reproof of the Hopf invariant one theorem. Despite this, secondary cohomology operations still see modern usage, for example, in the obstruction theory of commutative ring spectra. Examples of secondary and higher cohomology operations include the Massey product, the Toda bracket, and differentials of spectral sequences. (Wikipedia).
From playlist Courses and Series
Duality for Rabinowitz-Floer homology - Alex Oancea
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Duality for Rabinowitz-Floer homology Speaker: Alex Oancea Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche Date: May 27, 2020 For more video please visit http://video.ias.edu
From playlist PU/IAS Symplectic Geometry Seminar
Sheagan John: Secondary higher invariants, and cyclic cohomology for groups of polynomial growth
Talk by Sheagan John in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on December 2, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Graphing the Cosine Function with a Phase Shift
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From playlist How to Graph Trigonometric Functions
Solving for cosine by factoring
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From playlist Solve Trigonometric Equations
CDH methods in K-theory and Hochschild homology - Charles Weibel
Charles Weibel Rutgers University; Member, School of Mathematics November 11, 2013 This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assumi
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
Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators
HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a
From playlist Lie Theory and Generalizations
Sheel Ganatra: The Floer theory of a cotangent bundle, the string topology of the base and...
Find other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies,
From playlist Jean-Morlet Chair - Lalonde/Teleman
Moduli Spaces of Nodal Curves from Homotopical Algebra - Yash Deshmukh
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Moduli Spaces of Nodal Curves from Homotopical Algebra Speaker: Yash Deshmukh Affiliation: Columbia University Date: November 25, 2022 I will discuss how the Deligne-Mumford compactification of curves arises
From playlist Mathematics
Coproduct Structures, a Tale of Two Outputs - Lea Kenigsberg
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Coproduct Structures, a Tale of Two Outputs Speaker: Lea Kenigsberg Affiliation: Columbia University Date: November 25, 2022 I will motivate the study of coproducts and describe a new coproduct structure on
From playlist Mathematics
Graphing a Cosine Function with a Horizontal Shift
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From playlist How to Graph Trigonometric Functions
Learn How to Graph the Cosine Function with a Phase Shift
👉 Learn how to graph a cosine function. To graph a cosine function, we first determine the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the vertica
From playlist How to Graph Trigonometric Functions
Special Values of Zeta Functions (Lecture 1) by Matthias Flach
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Graph the Cosine Function with a Phase Shift
👉 Learn how to graph a cosine function. To graph a cosine function, we first determine the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the vertica
From playlist How to Graph Trigonometric Functions
Graphing a Trigonometric Graph Cosine with a Horizontal Shift
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From playlist How to Graph Trigonometric Functions
Graphing the Cosine Function with a Change in Period and Vertical Transformation
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From playlist How to Graph Trigonometric Functions
A Riemann-Roch theorem in Bott-Chern cohomology - Jean-Michel Bismut
Jean-Michel Bismut Université Paris-Sud April 21, 2014 If MM is a complex manifold, the Bott-Chern cohomology H(⋅,⋅)BC(M,C)HBC(⋅,⋅)(M,C) of MM is a refinement of de Rham cohomology, that takes into account the p,q p,q grading of smooth differential forms. By results of Bott and Chern, vect
From playlist Mathematics
How to solve an equation with cosine
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From playlist Solve Trigonometric Equations
Calista Bernard - Applications of twisted homology operations for E_n-algebras
An E_n-algebra is a space equipped with a multiplication that is commutative up to homotopy. Such spaces arise naturally in geometric topology, number theory, and mathematical physics; some examples include classifying spaces of braid groups, spaces of long knots, and classifying spaces of
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory