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111 Instead of an ordinary oriented $(n-1)$-manifold via the inward (or outward) normal |
111 Instead of an ordinary oriented $(n-1)$-manifold via the inward (or outward) normal |
112 first (or last) convention, perhaps it is better to define the boundary to be an $(n-1)$-manifold |
112 first (or last) convention, perhaps it is better to define the boundary to be an $(n-1)$-manifold |
113 equipped with an orientation of its once-stabilized tangent bundle. |
113 equipped with an orientation of its once-stabilized tangent bundle. |
114 Similarly, in dimension $n-k$ we would have manifolds equipped with an orientation of |
114 Similarly, in dimension $n-k$ we would have manifolds equipped with an orientation of |
115 their $k$ times stabilized tangent bundles. |
115 their $k$ times stabilized tangent bundles. |
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116 Probably should also have a framing of the stabilized dimensions in order to indicate which |
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117 side the bounded manifold is on. |
116 For the moment just stick with unoriented manifolds.} |
118 For the moment just stick with unoriented manifolds.} |
117 \medskip |
119 \medskip |
118 |
120 |
119 We have just argued that the boundary of a morphism has no preferred splitting into |
121 We have just argued that the boundary of a morphism has no preferred splitting into |
120 domain and range, but the converse meets with our approval. |
122 domain and range, but the converse meets with our approval. |