H-Spaces and Hopf Algebras - Mustafa HajijThe Cohomology algebra of an H-space is a Hopf algebra ....
Transcript of H-Spaces and Hopf Algebras - Mustafa HajijThe Cohomology algebra of an H-space is a Hopf algebra ....
H-Spaces and Hopf Algebras
Junior Topology Seminar Mustafa Hajij
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Algebras
Basic Def init ions
Hopf Algebras
Basic Def init ions
Hopf Algebras
Basic Def init ions
Hopf Algebras
Basic Def init ions
Hopf Algebras
Basic Def init ions
Hopf Algebras
Hopf Algebras
Example The Polynomial ring R[X]
Hopf Algebras
Example The Polynomial ring R[X]
Hopf Algebras
Example The Polynomial ring R[X]
Hopf Algebras
Example The Polynomial ring R[X]
Hopf Algebras
Example The Polynomial ring R[X]
Hopf Algebras
Example
Hopf Algebras
Example
Hopf Algebras
Example
Hopf Algebras
Example
Hopf Algebras
Example
Hopf Algebras
Example
Hopf Algebras
Example
H-Spaces
Definition of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
H-Spaces
Examples of H-spaces
The Cohomology algebra of an H-space is a Hopf algebra Introduction
The Cohomology algebra of an H-space is a Hopf algebra Introduction
The Cohomology algebra of an H-space is a Hopf algebra Introduction
The Cohomology algebra of an H-space is a Hopf algebra Introduction
The Cohomology algebra of an H-space is a Hopf algebra Introduction
The Cohomology algebra of an H-space is a Hopf algebra Dual Hopf Algebra
A Product structure on homology of H-spaces Pontryagin product
A Product structure on homology of H-spaces
Pontryagin product
A Product structure on homology of H-spaces
Pontryagin product
A Product structure on homology of H-spaces
Pontryagin product
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
Dual Hopf Algebra
What is the relation between Cohomology and Homology in H-spaces?
They are dual Hopf algebras
Dual Hopf Algebra
What is the relation between Cohomology and Homology in H-spaces?
They are dual Hopf algebras
Dual Hopf Algebra
T h a n k y o u