A virtual bundle with compact support is a triple ={,,},
where and are bundles over of the same dimension, is a closed manifold, is a bundle map from to , which is an isomorphism of bundles over , where is a compact set in M.
Let be a connection on , a connection on . If is finite number of points in , and Ch() is defined by , we will find Ch() integrated on is an integer multiple of a power of .
I want to know, if is a compact submanifold, then how to get the value of the integration? Maybe we can't get the value but how can we analyze the information about revealed by the integration?
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