Lecture

General Manifolds: A First Look

Related lectures (35)
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
General Manifolds and Topology
Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Dynamics of Steady Euler Flows: New Results
Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.
Differential Forms Integration
Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.
Smooth sets and functions: Example - atlas for a circleMOOC: Introduction to optimization on smooth manifolds: first order methods
Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Riemannian connections
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Forcing of Topological Entropy
Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.
Connections: motivation and definition
Explores the definition of connections for smooth vector fields on manifolds.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.