D. Husemller. Elliptic Curves (Graduate Text in Mathematics). Springer, ISBN: 0387954902, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....do not depend on the orientability or compactness of the base manifold (i.e. that T 0 M is always orientable, and that H 2n Gamma2 (T 0 M) and H 2n Gamma1 (T 0 M) are always torsion free) follow immediately from these results. All of the other results of Section 2 will depend on the Gysin sequence[11, 29]. Given a sphere bundle E B, there is an exact sequence : H k Gamman 1 (B; Z) H k (E) H k (B) H k Gamman (B; Z) where H (B; Z) indicates the homology of B with twisted coefficients. If 1 (B) acts trivially on H n Gamma1 (S ) then H (B; Z) H (B) but if the ....

....boundary map H n (M) H 0 (M ) If M is compact, connected and orientable, then H n (M) H 0 (M) Z. The boundary map is a homomorphism Z Z, which can also be thought of as multiplication by an integer. In fact, that integer is simply the Euler characteristic of M , M) P n fi i (M)[11]. The non trivial portion of the Gysin sequence becomes 0 H 1 (M) H n (T 0 M) Z Gamma Z H n Gamma1 (T 0 M) H n Gamma1 (M) 0: Combining this with H k (T 0 M) n 1 k 2n Gamma 1, we have ffl H 0 (T 0 M) H 2n Gamma1 (T 0 M) Z, 11 = H k n Gamma1 (T 0 M) for 2 ....

D. Husemoller, Fibre bundles, Graduate Texts in Mathematics, No. 20. Springer-Verlag, New YorkHeidelberg, 1975.

....;g is relatively compact in G. If every point of X has a wandering neighborhood then X is a Cartan G space [15, Definition 1.1.2] When the action is free, these spaces are precisely the principal bundles of Cartan by [15, Theorem 1.1. 3] and they are called principal G bundles by Husemoller in [13]. The action of G on X is proper (in the sense that the map (s; x) 7 (s Delta x; x) from G Theta X into X Theta X is a proper map) if and only if every compact subset of X is wandering. If the action of G on X is proper then X is a Cartan G space, but the converse is not true even if the ....

D. Husemoller, Fibre Bundles, Second ed., Springer-Verlag, New York, 1975, Graduate Texts in Mathematics, No. 20.

....on X. Then A = C 0 (X) oG is a Fell algebra if and only if X is a Cartan G space. Date: October 18, 1999. 1 2 AN HUEF When the action is free, the Cartan G spaces are precisely the principal bundles of Cartan by [5, Theorem 1.1. 3] and they are called principal G bundles by Husemoller in [4]. The action of G on X is proper (in the sense that the map (s; x) 7 (s Delta x; x) from G Theta X into X Theta X is a proper map) if and only if every compact subset of X is wandering. If the action of G on X is proper then X is a Cartan G space, but the converse is not true even if the ....

D. Husemoller, Fibre bundles, second ed., Springer-Verlag, New York, 1975, Graduate Texts in Mathematics, No. 20.

....6= g is relatively compact in G. If every point of X has a wandering neighborhood then X is a Cartan G space [15, De nition 1.1.2] When the action is free, these spaces are precisely the principal bundles of Cartan by [15, Theorem 1.1. 3] and they are called principal G bundles by Husemoller in [13]. The action of G on X is proper (in the sense that the map (s; x) 7 (s x; x) from G X into X X is a proper map) if and only if every compact subset of X is wandering. If the action of G on X is proper then X is a Cartan G space, but the converse is not true even if the action is free, an ....

D. Husemoller, Fibre bundles, second ed., Springer-Verlag, New York, 1975, Graduate Texts in Mathematics, No. 20.

....claim by means of bundle theory. On bundles. For the next step in rephrasing our problem we need some knowledge about bundles. We will only give the most basic de nitions and some examples to convey some feeling for the objects. An extensive introduction can be found in Dale Husemoller s book [6] on the subject. In this subsection we will not make any progress with respect to our problem, hence one can skip the subsection without any danger. De nition 3.1. An n dimensional (real or complex) vector bundle over the eld K 2 fR; C g is a triple = E; p; B) where p : E B is a ....

D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics 20, Springer Verlag, Berlin / New York, 1975

....claim by means of bundle theory. On bundles. For the next step in rephrasing our problem we need some knowledge about bundles. We will only give the most basic de nitions and some examples to convey some feeling for the objects. An extensive introduction can be found in Dale Husemoller s book [Hu75] on the subject. In this subsection we will not make any progress with respect to our problem, hence one can skip the subsection without any danger. 6 MARK DE LONGUEVILLE De nition 3.1. An n dimensional (real or complex) vector bundle over the eld K 2 fR; C g is a triple = E; p; B) where ....

....We were considering a (complex) n dimensional vector space E together with a unitary representation of G, which we consider as a left G action on E . Hence we 8 MARK DE LONGUEVILLE have an associated bundle [E ] ENG G E ENG E= xg; y) x; gy) y p BN G: It is a well known fact (cf. Hu75] p. 48) that sections S : BNG ENG G E of such bundles are in bijective correspondence with continuous maps s : ENG E such that s(x g 1 ) g s(x) for x 2 ENG, g 2 G. The section corresponding to s is given by S( x] G ) x; s(x) G , where the brackets denote the appropriate ....

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D. Husemoller, Fibre Bundles, Graduate Texts in Mathematics 20, Springer Verlag, Berlin / New York 1975

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D. Husemller. Elliptic Curves (Graduate Text in Mathematics). Springer, ISBN: 0387954902, 1987.

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D. Husemoller, Elliptic curves, Graduate Texts in Mathematics, vol. 111, Springer-Verlag, 1987.

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D. Husemoller, Fibre bundles, Graduate Texts in Mathematics 20, Springer (1994) 33

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S. Lang. Elliptic Functions. Graduate Texts in Mathematics, vol. 112 (Springer-Verlag, 1987).

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D. Husemoller, Elliptic curves, Graduate Texts in Mathematics, vol. 111, Springer-Verlag, 1987.

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