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is a component of the branched surface minus its branching set. Weights are assigned so that if a component branches into two other components, then the sum of the weights of the two unidentified halfplanes of that neighborhood is the weight of the identified halfplane.
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Shields, Sandra. "The stability of foliations of orientable 3-manifolds covered by a product." Transactions of the
American Mathematical Society 348.11 (1996): 4653-4671.
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and glue it and A together along halfspaces so that the singular line of this gluing is transverse in A to the previous singular line.
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of each with a closed half-space of the other. This will be a surface except along a single line. Now, pick another copy C of
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Li, Tao. "Laminar
Branched Surfaces in 3-manifolds." Geometry and Topology 6.153 (2002): 194.
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does not include any points whose only neighborhoods are the quotient space described above.
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Consider, however, the space obtained by taking the
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is maximal with respect to the above two conditions.
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169:; if this is done, the space is often called a
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153:is a space that is locally modeled on K.
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120:under the identification of a closed
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44:is a space that locally looks like
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149:Call this complicated space K. A
113:{\displaystyle \mathbb {R} ^{2}}
66:{\displaystyle \mathbb {R} ^{2}}
161:A branched manifold can have a
177:and are assigned to subspaces
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181:that satisfy the following:
139:{\displaystyle \mathbb {R} }
24:is a generalization of both
173:. Weights are non-negative
165:assigned to various of its
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171:weighted branched manifold
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278:Generalized manifolds
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91:of two copies A,B of
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268:Geometric topology
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224:Branched manifold
219:Branched covering
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30:train tracks
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273:3-manifolds
18:mathematics
262:Categories
230:References
122:half-space
36:Definition
204:That is,
167:subspaces
213:See also
188:is open.
89:quotient
26:surfaces
42:surface
163:weight
157:Weight
79:up to
84:).
28:and
20:, a
73:(a
16:In
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40:A
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206:N
198:N
192:N
186:N
179:N
133:R
106:2
101:R
59:2
54:R
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