Concept

Torus

Related lectures (18)

Explores three ways to form quotient spaces using group actions and equivalence relations.

Explores the connected sum of surfaces, focusing on torus and RP2, highlighting the resulting homeomorphism with the sphere.

Surface Classification

Covers the classification of surfaces using polygonal presentations and homeomorphism.

Homotopy Extension Property

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

Cellular structure of the torus with two holes

Explores the cellular structure of the torus with two holes.

Homotopy: Fundamentals and Examples

Covers the fundamentals of homotopy and its applications in topology.

Topology: Disk Deprivation

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

Elliptic Curves: Group Structure and Isomorphism

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

The Two-Holed Torus

Covers the construction of the connected sum of two tori in 10 minutes.

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

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.

Topology: Fundamental Groups and Surfaces

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

Ray Tracing: Fundamentals

Covers the basics of ray tracing, including ray generation, intersection with geometric shapes, and distance calculations to planes, setting the foundation for implementing a ray tracer.

Symmetric Product Orbifolds & Holography

Explores Symmetric Product Orbifolds and their relation to Holography in AdS/CFT duality, covering AdS3 Gravity, primary operators, and BPS states.

Forcing of Topological Entropy

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Homotopy Theory: Cylinders and Path Objects

Covers cylinders, path objects, and homotopy in model categories.

Essential Coexistence Phenomenon in Hamiltonian Dynamics

By Yakov Pesin delves into the essential coexistence phenomenon in Hamiltonian dynamics, exploring types I and II and providing examples and proofs.

Construction of the homotopy category

Explains the construction of the homotopy category of a model category using cofibrant and fibrant replacement.