Normal maps - (non)-examples (Ex)

Revision as of 08:37, 6 January 2019

1) Give an example of a degree one map of closed $<wikitex>; 1) Give an example of a degree one map of closed $n$-manifolds $f \colon M \to X$ which cannot be covered by a map $\overline{f} \colon \nu_M \to \nu_X$ of normal bundles. 2) For every integer $d$, give an example of a degree $d$ map $f_d \colon M \to X$ of closed $n$-manifolds which can be covered by a map $\overline{f_d} \colon \nu_M \to \nu_X$ of normal bundles. 3) Let $F_g$ denote the oriented surface of genus $g$. Determine the values of $(g, g')$ for which there is a degree one normal map $(f, \overline{f}) \colon F_g \to F_{g'}$. </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]n$-manifolds $f \colon M \to X$ which cannot be covered by a map $\overline{f} \colon \nu_M \to \nu_X$ of normal bundles.

2) For every integer $d$, give an example of a degree $d$ map $f_d \colon M \to X$ of closed $n$-manifolds which can be covered by a map $\overline{f_d} \colon \nu_M \to \nu_X$ of normal bundles.

3) Let $F_g$ denote the oriented surface of genus $g$. Determine the values of $(g, g')$ for which there is a degree one normal map $(f, \overline{f}) \colon F_g \to F_{g'}$.

References