Normal maps - (non)-examples (Ex)
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(Created page with "<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 b...") |
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− | + | 1a) 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. | |
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+ | 1b) Give an example of a degree one map of closed $n$-manifolds $f \colon M \to X$ which cannot be covered by a map $\overline{f} \colon \nu_M \to \xi$ of bundles, for any stable bundle $\xi$. | ||
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. | 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. | ||
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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 $(f, \overline{f}) \colon F_g \to F_{g'}$. | 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 $(f, \overline{f}) \colon F_g \to F_{g'}$. | ||
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− | == References == | + | <!-- == References== |
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[[Category:Exercises]] | [[Category:Exercises]] | ||
− | [[Category:Exercises | + | [[Category:Exercises with solution]] |
Latest revision as of 07:43, 10 January 2019
1a) Give an example of a degree one map of closed -manifolds which cannot be covered by a map of normal bundles.
1b) Give an example of a degree one map of closed -manifolds which cannot be covered by a map of bundles, for any stable bundle .
2) For every integer , give an example of a degree map of closed -manifolds which can be covered by a map of normal bundles.
3) Let denote the oriented surface of genus . Determine the values of for which there is a degree one normal map .