Normal maps and submanifolds (Ex)

Revision as of 10:26, 24 February 2012

Let $<wikitex>; 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: # There is a canonical degree one normal map $(f|N, b') \colon (N, \nu) \to (Y, \xi|Y \oplus \nu_{Y \subset X})$. # ... </wikitex> == References == {{#RefList:}} [[Category:Exercises]](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 $k$ 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. ...

References