Lectures related to Exact sequence

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Long Exact Sequence of Ext-Modules

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

Exact Linearization: Determining Conditions and Transformations

Explores exact linearization, determining conditions and transformations using Lie bracket and hook of Lie.

Mayer-Vietoris Sequence

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Long Exact Sequence of Ext-Modules

Covers the construction of long exact sequences of Ext-modules and provides illustrative examples.

Simplicial and Singular Homology Equivalence

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Naturality: Chain Complexes and Homology Groups

Explores naturality in chain complexes, homology groups, and abelian groups, emphasizing the commutativity of squares and the Five-Lemma.

Exact Sequences in Abelian Groups

Explains split exact sequences in abelian groups, emphasizing the role of sections and retractions.

Exact Sequences in Abelian Groups

Covers exact sequences of homomorphisms in abelian groups, including injective sequences and split sequences.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Curl and Exact Sequences

Covers the concept of curl in vector calculus and De Rham cohomology.

Sylow Subgroups: Structure and Properties

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Exact Sequences: Torsion and Divisibility

Explores exact sequences of abelian group homomorphisms and provides examples.

Topology: Lecture Notes 2021

Covers commutative diagrams, homotopy, and constructing topological spaces.

Group Presentations: Abelian Groups

Covers exact sequences, torsion, divisibility, and operations on abelian groups.

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.

Exact Sequences: Splitting Remarks

Explores split exact sequences in group theory with a focus on characterization and isomorphisms.

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.