- #1
dkotschessaa
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Another zany homology question:
Just let me know if I have my labeling scheme right so far.
I have a torus. I have cut two holes into it and am attaching Möbius strips around the holes. (Clearly we are not in 3 dimensions?)
My Torus is represented by a polygon with the labeling scheme ## a b a^{-1}b^{-1} ## and my strips are labeled ## a b c b ## as follows (I'll subscript them after pasting)
I'll subscript the torus with 1s, and the 2 mobius strips will be subscripted with 2s and 3s.
I think I cut a hole in the Torus just by cutting a corner off of the polygon. I'll attach the strips to attain the following monstrosity:
I end up with a long labeling scheme:
##a_1 b_1 c_1 b_2 b_1 b_3 c_3 b_3 a_1^{-1} b_1^{-1} ##
Before I say any further, is this what cutting a hole in a Torus and gluing a Möbius band even would look like? Obviously I can't picture this outside the polygons here. Thanks for your patience.
-Dave K
Just let me know if I have my labeling scheme right so far.
I have a torus. I have cut two holes into it and am attaching Möbius strips around the holes. (Clearly we are not in 3 dimensions?)
My Torus is represented by a polygon with the labeling scheme ## a b a^{-1}b^{-1} ## and my strips are labeled ## a b c b ## as follows (I'll subscript them after pasting)
I'll subscript the torus with 1s, and the 2 mobius strips will be subscripted with 2s and 3s.
I think I cut a hole in the Torus just by cutting a corner off of the polygon. I'll attach the strips to attain the following monstrosity:
##a_1 b_1 c_1 b_2 b_1 b_3 c_3 b_3 a_1^{-1} b_1^{-1} ##
Before I say any further, is this what cutting a hole in a Torus and gluing a Möbius band even would look like? Obviously I can't picture this outside the polygons here. Thanks for your patience.
-Dave K