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From: bacle on 7 Jun 2010 20:28
Hi, everyone:

I am trying to understand better the definition of
a quotient bundle, from a paper. Please comment
on wether my understanding/interpretation is correct;
here is the def, and below is my interpretation:

"Given a smooth manifold X with tangent bundle T_X,
and a submanifold Y<X , we get a fibrewise
inclusion, and a quotient bundle T_X|Y/ T_Y ,
defined by the sequence :

0-->T_Y -->TX|Y -->Q_Y/X -->0 "

Where X|Y is the restriction of X to Y, i.e.,given

the bundle p:E-->X , and Y<X , we define

T_X|Y as a bundle with total space p^-1(Y) , and

projection map p^=p|_(p^-1(Y)) , i.e., p^ is the

restriction of p to p^-1(Y) .

** Question** : is Q , as defined in the SES above,

the bundle whose fiber is the quotient vector space of

the tangent space at X , restricted to Y by the

tangent space at Y.?


Thanks.
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