Talk:Borel Conjecture for the 2-torus (Ex)
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| − | Suggestion: | + | Suggestion 1: |
1. Note that the dimensions must be equal. | 1. Note that the dimensions must be equal. | ||
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3. Use the square model for the torus with edges identified, lying in a grid. Assume WLOG that the map preserves orientation (if not, then flip it). Homotope the map to the identity map. | 3. Use the square model for the torus with edges identified, lying in a grid. Assume WLOG that the map preserves orientation (if not, then flip it). Homotope the map to the identity map. | ||
</wikitex> | </wikitex> | ||
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| + | Suggestion 2: | ||
| + | Do not use Suggestion 1. | ||
Revision as of 06:33, 10 January 2019
Suggestion 1:
1. Note that the dimensions must be equal.
2. Use the homotopy classification of surfaces, so both surfaces must be 
.
3. Use the square model for the torus with edges identified, lying in a grid. Assume WLOG that the map preserves orientation (if not, then flip it). Homotope the map to the identity map.
Suggestion 2: Do not use Suggestion 1.
