Lectures related to Pointed space

Fundamental Group of a Product

Covers the calculation of the fundamental group of a product using small spaces and compositions.

Topology: Seifert van Kampen Theorem

Explores the Seifert van Kampen theorem and its applications in calculating fundamental groups.

Topology: Disk Deprivation

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.

Induced Homomorphisms on Relative Homology Groups

Covers induced homomorphisms on relative homology groups and their properties.

Homotopy Extension Property

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Topology: Fundamental Groups and Surfaces

Discusses fundamental groups, surfaces, and their topological properties in detail.

Pointed Mapping Spaces: Exponential Law and Adjunction

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Well Pointed Spaces and Wedge

Discusses well pointed spaces, neighborhoods, wedges, examples, and the universal property of the quotient.

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Knot Theory: The Quadratic Linking Degree

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Contracting Subspaces

Explores the homotopy extension property for contractable subspaces and their quotient maps.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Group Morphisms: G-equivariant, Chapter III

Discusses the formulation of G-morphisms within vector spaces and topological spaces.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.