Normal maps and submanifolds (Ex)
(Difference between revisions)
m |
m |
||
Line 1: | Line 1: | ||
<wikitex>; | <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 $k$ | + | 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 $k$ 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 $(f|N, b') \colon (N, \nu) \to (Y, \xi|Y \oplus \nu_{Y \subset X})$. | # There is a canonical degree one normal map $(f|N, b') \colon (N, \nu) \to (Y, \xi|Y \oplus \nu_{Y \subset X})$. | ||
# ... | # ... |
Revision as of 10:26, 24 February 2012
Let be a degree one normal map. For simplicity, assume that and are closed oriented -manifolds of dimension . Suppose that is a codimension oriented submanifold with normal bundle and that that is transverse to . Prove the following:
- There is a canonical degree one normal map .
- ...