Talk:Borel Conjecture for the 2-torus (Ex)
(Difference between revisions)
(Created page with "<wikitex>; Suggestion: 1. Note that the dimensions must be equal. 2. Use the homotopy classification of surfaces, so both surfaces must be $T^2$. 3. Use the square model fo...") |
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2. Use the homotopy classification of surfaces, so both surfaces must be $T^2$. | 2. Use the homotopy classification of surfaces, so both surfaces must be $T^2$. | ||
| − | 3. Use the square model for the torus with edges identified. Assume WLOG that the map preserves orientation. | + | 3. Use the square model for the torus with edges identified, lying in a grid. Assume WLOG that the map preserves orientation. Homotope the map to the identity map. |
</wikitex> | </wikitex> | ||
Revision as of 06:56, 9 January 2019
Suggestion:
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. Homotope the map to the identity map.
