Coordinate Patches
February 23, 2011  Posted by John Armstrong  Differential Topology, Topology
3 Comments »
Leave a Reply Cancel reply
About this weblog
This is mainly an expository blath, with occasional highlevel excursions, humorous observations, rants, and musings. The mainline exposition should be accessible to the “Generally Interested Lay Audience”, as long as you trace the links back towards the basics. Check the sidebar for specific topics (under “Categories”).
I’m in the process of tweaking some aspects of the site to make it easier to refer back to older topics, so try to make the best of it for now.

Recent Posts
 The Submodule of Invariants
 More New Modules from Old
 New Modules from Old
 Reducible Modules
 Irreducible Modules
 Lie Algebra Modules
 All Derivations of Semisimple Lie Algebras are Inner
 Decomposition of Semisimple Lie Algebras
 Back to the Example
 The Radical of the Killing Form
 The Killing Form
 Cartan’s Criterion
 A Trace Criterion for Nilpotence
 Uses of the JordanChevalley Decomposition
 The JordanChevalley Decomposition (proof)
Blogroll
Art
Astronomy
Computer Science
Education
Mathematics
 A Dialogue on Infinity
 A Singular Continuity
 Ars Mathematica
 Carter and Complexity
 Curious Reasoning
 Fightin’ the resistance of matter
 God Plays Dice
 Good Math, Bad Math
 Gowers's Weblog
 Gyre&Gimble
 Intrinsically Knotted
 Low Dimensional Topology
 Mathematics and physics
 Mathematics under the Microscope
 Michi’s blog
 Really Hard Sums
 Rigorous Trivialities
 Secret Blogging Seminar
 Sketches of Topology
 Steven Strogatz
 Sumidiot
 The Everything Seminar
 The Museum of Mathematics
 The nCategory Café
 The Universe of Discourse
 Theoretical Atlas
 This Week's Finds in Mathematical Physics
 Topological Musings
 What's new
Me
Philosophy
Physics
Politics
Science
RSS Feeds
Feedback
Got something to say? Anonymous questions, comments, and suggestions at Formspring.me!Subjects
Archives
Site info
The Unapologetic MathematicianThe Andreas04 Theme. Create a free website or blog at WordPress.com.
[…] thought to be sure about. Specifically, our definition says that each point is contained in some coordinate patch , which comes with a coordinate map . But does the here have to be the same for all points […]
Pingback by The Dimension of a Manifold « The Unapologetic Mathematician  February 24, 2011 
[…] and be two coordinate patches on an manifold . We can restrict each coordinate map to the intersection of the two patches […]
Pingback by Classes of Manifolds « The Unapologetic Mathematician  February 25, 2011 
[…] say we have a coordinate patch around a point in an dimensional manifold . We can use the function to give us some tangent […]
Pingback by Tangent Vectors and Coordinates « The Unapologetic Mathematician  March 30, 2011 