Normal maps and submanifolds (Ex)

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Let (f, b) \colon (M, \nu_M) \to (X, \xi) be a degree one normal map. For simplicity, assume that M and X are closed oriented \text{Cat}-manifolds of dimension n. Suppose that Y \subset X is a codimension k submanifold oriented submanifold X with normal bundle \nu_{Y \subset X} and that that f is transverse to Y. Prove the following:

  1. There is a canonical degree one normal map (f|N, b') \colon (N, \nu) \to (Y, \xi|Y \oplus \nu_{Y \subset X}.
  2. ...


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