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108 and collaring maps, |
108 and collaring maps, |
109 the gluing map is surjective. |
109 the gluing map is surjective. |
110 We say that fields on $X\sgl$ in the image of the gluing map |
110 We say that fields on $X\sgl$ in the image of the gluing map |
111 are transverse to $Y$ or splittable along $Y$. |
111 are transverse to $Y$ or splittable along $Y$. |
112 \item Gluing with corners. |
112 \item Gluing with corners. |
113 Let $\bd X = Y \cup Y \cup W$, where the two copies of $Y$ and |
113 Let $\bd X = (Y \du Y) \cup W$, where the two copies of $Y$ |
114 $W$ might intersect along their boundaries. \todo{Really? I thought we wanted the boundaries of the two copies of Y to be disjoint} |
114 are disjoint from each other and $\bd(Y\du Y) = \bd W$. |
115 Let $X\sgl$ denote $X$ glued to itself along the two copies of $Y$ |
115 Let $X\sgl$ denote $X$ glued to itself along the two copies of $Y$ |
116 (Figure \ref{fig:???}). |
116 (Figure \ref{fig:???}). |
117 Note that $\bd X\sgl = W\sgl$, where $W\sgl$ denotes $W$ glued to itself |
117 Note that $\bd X\sgl = W\sgl$, where $W\sgl$ denotes $W$ glued to itself |
118 (without corners) along two copies of $\bd Y$. |
118 (without corners) along two copies of $\bd Y$. |
119 Let $c\sgl \in \cC_{k-1}(W\sgl)$ be a be a splittable field on $W\sgl$ and let |
119 Let $c\sgl \in \cC_{k-1}(W\sgl)$ be a be a splittable field on $W\sgl$ and let |