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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
micromass
1 26,448
I asked this question over in the QM forum, but it fizzled out there. I think it's more appropriate here anyway so...
Feb28-10 07:48 PM
Talisman
8 1,970
What is a very good differential geometry introductory text? My only background is Calculus (spivak). however, I'm...
Jul25-09 08:23 AM
slider142
8 6,337
I read this: A class T of subsets of X is called a topology on X if it satisfies these 2 conditions: 1. The union of...
Jul10-09 10:41 AM
symbol0
8 1,436
Hi! I'm trying to learn some geometry for general relativity, and I am having a bit of trouble understanding how to...
Aug11-09 07:46 PM
HallsofIvy
8 2,373
I've been reading Shilov's book and the definition of a limit point is as follows: x is a limit point of A if every...
Dec20-09 10:51 PM
haider ali
8 3,735
Seen a couple of pieces on gauge theories of finance equating arbitrage opportunities to curvature, for this to work...
Sep2-09 12:17 AM
zhentil
8 1,317
What should one know before reading this textbook? I have taken a course in differential topology (it was called...
Sep2-09 06:06 AM
wofsy
8 2,281
hi there What is a Poincare' disc and why is the edges of disc represent infinity? thanks
Oct9-09 02:19 PM
wofsy
8 1,698
Using the Mayer–Vietoris sequence, how can we calculate the De Rham cohomology of the Kelin bottle?
Oct15-09 09:17 AM
TFT
8 3,401
Dear all, I've always wondered where the name "manifold" comes from? Any idea? Thanks, Goldbeetle
Dec10-09 05:33 AM
HallsofIvy
8 3,002
I have a question here and i'm not sure what to do as it always confuses me, any help? Let A,B be closed non-empty...
Jan7-10 01:38 PM
madness
8 2,925
Hello, if one wants to represent a parametric curve in a N-dimensional vector space, the straightforward way is to...
Feb15-10 04:48 AM
Fredrik
8 1,494
Is this a cone after Identifaction? Let A = (I × I)/J where J = (I × {1}) ∪ ({0; 1} × I) ⊂ I × I
Feb24-10 07:43 AM
Mikemaths
8 2,217
Ok, I need some math info and I think this is the right section for my question, but I may be wrong. Is it physics?...
Mar17-10 04:13 PM
Hoku
8 1,369
I've been trying to get a grasp on Lie Derivatives. I understand that we can represent a lie derivative acting on a...
Apr1-10 09:56 AM
linford86
8 1,535
After a century time, the millennium of Poincaré Conjecture has been solved by Dr. Grigoriy Perelman. ...
Mar25-10 10:01 AM
TFT
8 4,456
Hello, I am a newbie of this forum. Nice to meet you all. When I read mathematical proofs or whatever, I always...
Apr19-10 03:20 PM
Tac-Tics
8 2,388
Electric charge continuity is expressed as ∂tρ + ∂iJi =0. (1) The manifold, M in question is 3 dimensional and t is...
Apr28-10 12:43 PM
Phrak
8 3,379
If I take a plane with n holes, would the fundamental group be that of the "bouquet of n circles"?...
Apr24-10 07:40 PM
Bacle
8 3,267
Hi: Just curious: a continuous function f:X-->Y ; X,Y topological spaces, can fail to be an embedding because...
May25-10 04:36 PM
Landau
8 2,877
Hi, everybody: I have read different sources for quotient bundle: Milnor and Stasheff, Wikipedia Wolfram,...
May19-10 01:44 PM
lavinia
8 2,298
I'm a beginner at differential geometry. I have a problem about dual space. I understand why we use...
May22-10 04:34 AM
haushofer
8 2,716
Given points A(x1, y1) and B(x2, y2), I'm supposed to derive the coordinate of the point C which should be on the...
Jun30-10 04:59 PM
SonyAD
8 2,422
Hello all, I feel a bit out of my league here :) if I've posted in the wrong section I'm so sorry... I am looking...
Jun13-10 10:49 PM
Phrak
8 1,840
I am new to this subject of topology. I want to know if bending and stretching of a manifold is same as a general...
Jun28-10 05:28 AM
lavinia
8 1,622
Hi all, I'm a physicist attempting to learn twistor theory. I'm confused by this notion of a tautological line...
Jul7-10 10:29 AM
chrispb
8 2,243
Is a curve (Say 'S') 1d or 2d? I ask this question because for so long i was under the impression that it was 2d,...
Jul14-10 05:59 AM
asdfghjklqqww
8 1,352
it is easy to construct a map from S^2 to S^2, with covering time being unity but how to do the similar task on the...
Jul23-10 08:40 AM
wdlang
8 1,075
Hello all, I am a newbie to topology. Hope someone can help sharpen my understanding. I read a theorem that "if ...
Jul22-10 05:53 PM
wayneckm
8 2,378
Is there a relationship between the homotopy groups of a pair (X,A) and of the quotient X/A ? It feels like they...
Aug1-10 11:12 PM
quasar987
8 1,440
They aren't equivalent in general, but do they ever coincide, and, if so, under what conditions? I've seen both...
Aug27-10 05:33 PM
Rasalhague
8 1,700
Hi, I have some doubts about the precise meaning of Euclidean space. I understand Euclidean space as the metric...
Aug28-10 05:12 PM
Hurkyl
8 3,475
I'm trying to do a project that requires me construct a circle with n chords. I need to find the maximum number of...
Oct2-10 08:00 PM
quasar987
8 2,034
Do you agree that the following identity is true: \int_S (\nabla_\mu X^\mu) \Omega = \int_{\partial S} X \invneg ...
Oct24-10 07:06 AM
arkajad
8 2,108
I get in essence what the covariant derivative is, and what it does, but im having trouble with the definition, of all...
Oct24-10 02:21 AM
Phrak
8 1,207
Hello, if we consider the stereographic projection \mathcal{S}^2\rightarrow \mathbb{R}^2 given in the form: (X,Y)...
Nov16-10 05:06 AM
tiny-tim
8 2,352
I'm self studying some alg topology for next semester just working through chapter 0 and 1 of hatcher really. My...
Nov23-10 06:07 AM
quasar987
8 2,104
Here's just a conceptual question about this proof. One can show a space is X metrizable by embedding it into a...
Dec19-10 04:35 PM
micromass
8 2,608
I am looking for an example of a 4 dimensional compact smooth manifold that has the following properties - it is...
Jan8-11 11:14 AM
lavinia
8 1,600
So, in Munkres' chapter about the Stone-Čech compactification, there is a Lemma at the beginning of the chapter the...
Dec26-10 05:00 PM
radou
8 873

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