李代数胚的奇异特征同态
Some Exotic Characteristic Homomorphism for Lie Algebroids
摘要：
作者定义了三元组（A，B，\bigtriangledown）的一些次特征同态，其中B \subset A是同一个叶状流形上的一对正则李代数胚，而\bigtriangledown：L \rightarrow A是李代数胚的同态（即A中的平坦L-联络），其中L是任意的（不一定是正则的）李代数胚，并证明了来自其像的特征类推广了平坦正则李代数胚（Kubarski）和具有约化的平坦主纤维丛（Kamber，Tondeur）的已知奇异特征类。推广也包括一个由Crainic表示的李代数胚的向量丛。对于正则李代数胚对\subset A和平坦联络id：\rightarrow A的特殊情况，我们得到了一个特征同态，它是任意平坦L-联络\bigtriangledown的任何其它同态的因子，在这个意义上它是泛同态：\rightarrow A.
英文摘要：
The authors define some secondary characteristic homomorphism for the triple (A,B,\bigtriangledown), in which B\subset A is a pair of regular Lie algebroids over the same foliated manifold and \bigtriangledown:L\rightarrow A is a homomorphism of Lie algebroids (i.e. a flat L-connection in A) where L is an arbitrary (not necessarily regular) Lie algebroid and show that characteristic classes from its image generalize known exotic characteristic classes for flat regular Lie algebroids (Kubarski) and flat principal fibre bundles with a reduction (Kamber, Tondeur). The generalization includes also the one given by Crainic for representations of Lie algebroids on vector bundles. For a pair of regular Lie algebroids B \subset A and for the special case of the flat connection id:A\rightarrow A we obtain a characteristic homomorphism which is universal in the sense that it is a factor of any other one for an arbitrary flat L-connection \bigtriangledown:L\rightarrow A.
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