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95 |
95 |
96 \nn{Note: We have to decide whether our 2-morphsism are shaped like rectangles or bigons. |
96 \nn{Note: We have to decide whether our 2-morphsism are shaped like rectangles or bigons. |
97 Each approach has advantages and disadvantages. |
97 Each approach has advantages and disadvantages. |
98 For better or worse, we choose bigons here.} |
98 For better or worse, we choose bigons here.} |
99 |
99 |
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100 \nn{maybe we should do both rectangles and bigons?} |
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101 |
100 Define the $k$-morphisms $C^k$ of $C$ to be $\cC(B^k)_E$, where $B^k$ denotes the standard |
102 Define the $k$-morphisms $C^k$ of $C$ to be $\cC(B^k)_E$, where $B^k$ denotes the standard |
101 $k$-ball, which we also think of as the standard bihedron. |
103 $k$-ball, which we also think of as the standard bihedron. |
102 Since we are thinking of $B^k$ as a bihedron, we have a standard decomposition of the $\bd B^k$ |
104 Since we are thinking of $B^k$ as a bihedron, we have a standard decomposition of the $\bd B^k$ |
103 into two copies of $B^{k-1}$ which intersect along the ``equator" $E \cong S^{k-2}$. |
105 into two copies of $B^{k-1}$ which intersect along the ``equator" $E \cong S^{k-2}$. |
104 Recall that the subscript in $\cC(B^k)_E$ means that we consider the subset of $\cC(B^k)$ |
106 Recall that the subscript in $\cC(B^k)_E$ means that we consider the subset of $\cC(B^k)$ |