Example 2.10 (Positive fibration) . [04HU]
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Example 2.10 (Positive fibration).
This model is the other possible fibration over a neighborhood of a point in –in [7] this is called fibration. Let with and as in Example 2.8. Let , where . Let and define . Now consider a principal -bundle . Under some mild assumptions on (cf. [7] Prop. 2.9), there is a unique manifold with extending the topology of and a proper extension of . The composition of with the projection defines a topological -fibration, . The fibre of over is . The fibre over is homeomorphic to , whereas the fibre over the vertex is homeomorphic to . It is proved in [7] that the monodromy group of this model is generated, in some basis, by the inverse transpose of the matrices (3). The reader should not worry, at this point, for the lack of details in this description as we will give explicit Lagrangian models for this example later on.