Homology Tangent Bundles and Universal Bundles
نویسندگان
چکیده
منابع مشابه
Homology Tangent Bundles and Universal Bundles1
We find results about the evaluation map from the group of homeomorphisms of a closed manifold M and also about fibre bundles where M is the fibre. These facts follow from the observation that the homology tangent bundle is induced from a universal bundle pair.
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i) 8 (p;Xp) 2 TM , as p 2M ) there exists (U ; ) 2 S such that p 2 U ; i.e. (p;Xp) 2 TU , and we have TU = 1 (R) 2 . ii) If we de ne F : TpM ! R by F (Xp) = (Xp(x); Xp(x); :::::; Xp(x)) where x; x; ::::; x are local coordinates on (U ; ), then clearly F is an isomorphism, so (p; Xp) = ( (p); F ( Xp)); and 1 = ( 1 ; F 1 ). Now take 1 (U); 1 (V ) 2 and suppose (p; Xp) 2 1 (U)\ 1 (V ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1972
ISSN: 0002-9939
DOI: 10.2307/2039068