Lectures related to Topology in Computer-Aided Design

Delves into topology, homomorphism, and their practical implications on CAD software.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Covers course notes on topology, discussing Stasheff Mérida, cost-savings, and representative points.

Covers exercises on attaching 1-cells to intervals in topology.

Covers cell attachment, homotopy, mappings, and universal properties in topology.

Explores continuous deformations in topology, emphasizing the preservation of shape characteristics during transformations.

Explains the concept of the connected sum of surfaces through gluing and mathematical definitions.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Explores the power of a point outside a circle and its practical applications.

Covers homotopy, quotient spaces, and the universal property in topology.

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Covers the Hairy Ball Theorem and vector fields on spheres.

Covers the definition of edges, vertices, and cells in geometric shapes.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

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

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.