- #1
wdlang
- 307
- 0
take a circle in a plane
identify two opposite points
we get the projected space DP1
about the homotopy group of DP1, i have two answers
first, we take the upper semicircle from 0 to pi, and identify 0 with pi, by this way, we get a circle again. So the homotopy of DP1 should be identical to that of the circle, which is Z.
second, it is often shown that the only loop in DP1 that cannot be shrank to a point is the open route from 0 to pi
i am really puzzled
identify two opposite points
we get the projected space DP1
about the homotopy group of DP1, i have two answers
first, we take the upper semicircle from 0 to pi, and identify 0 with pi, by this way, we get a circle again. So the homotopy of DP1 should be identical to that of the circle, which is Z.
second, it is often shown that the only loop in DP1 that cannot be shrank to a point is the open route from 0 to pi
i am really puzzled