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Low Dimensional Topology

During this quantity, that's devoted to H. Seifert, are papers in accordance with talks given on the Isle of Thorns convention on low dimensional topology held in 1982.

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Now that we know that Pic(MGe;X ) = OMG;X e (1)Z we may ask what happens to our determinant bundle D. 1. Lemma. Let D be the determinant line bundle on MSLr ;X . Then D = OMSLr ;X (1) Proof. 1: ' QSLr G P1C ● ●● ●● ● ●●●5   MSLr ;X Using , we get a family E of SLr -bundles parameterized by P1C and, by the above, we have to show that the determinant line bundle of this family is OP1C (1). 2 and the remarks following it. Then E[a:c] is de ned by the inclusion   1 W = bzd cza (C [[z]]  C [[z]]) ,!

4 a) that (LG)o is isomorphic to LG= 9. The ind-group of loops coming from the open curve Let G be a connected simple complex group, X be a connected smooth projective complex curve. 1. 1. The simply connected case. 1. Proposition. 1) The ind-group LX Ge is integral. Proof. To see that LX Ge is reduced, consider the morphism  : QGe ! 1. Hence, locally for the etale topology,  is U  LX Ge ! U . 1 (iv). To prove that LX Ge is irreducible it is enough, as connected ind-groups are irreducible by Proposition 3 of [24], to show that LX Ge is connected.

39:19{55, 1976. [12] S. Kumar, M. S. Narasimhan, and A. Ramanathan. In nite Grassmannians and moduli spaces of G-bundles. Math. , 300(1):41{75, 1994. [13] Y. Laszlo. Linearization of group stack actions and the Picard group of the moduli of slr =s -bundles on a curve. Bull. Soc. Math. France, 125(4):529{545, 1997. [14] Y. Laszlo and C. Sorger. The line bundles on the moduli of parabolic G-bundles  Norm. Sup. (4), 30(4):499{525, 1997. over curves and their sections. Ann. Sci. Ecole [15] G. Laumon and L.

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