Register to reply

Fundamental group of matrices

by mich0144
Tags: fundamental, matrices
Share this thread:
mich0144
#1
Dec17-10, 01:01 AM
P: 19
why is S^n/S^m homotopic to S^n-m-1. the book just made this remark how do you see this geometrically.

how do you compute fundamental groups of matrices like O(3) and SO(3) or SL(2) and whatnot.
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
Bacle
#2
Dec19-10, 01:15 PM
P: 662
If I understand you well, when, you do a quotient S^n/S^m ; n>= m, you
identify S^m (seen as a subspace of S^n ) to a point. This collapses
a subset/subspace of S^n to a single point, which (meaning
self-intersection ) does not happen in S^k.

Re O(n) , etc., AFAIK, you identify them as a subset of points in R^n,
or , if you know any of these is the covering space of some top space X, you
may, e.g., use a SES in homotopy given by fibration, or properties of covering spaces.

Maybe someone else can expand on this.

HTH.


Register to reply

Related Discussions
Gamma matrices out of pauli matrices - symmetry/group theory Atomic, Solid State, Comp. Physics 0
Fundamental group to second homology group Differential Geometry 2
Fundamental Group of Matrices Differential Geometry 3
Fundamental matrices in inhomogenous problems? Differential Equations 0