Introductory Map Theory by Yanpei Liu PDF

By Yanpei Liu

ISBN-10: 1599731347

ISBN-13: 9781599731346

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This is the sufficiency. 1.

A vertex around five, six or seven triangular disks is called an elliptic vertex, an Euclidean vertex or a hyperbolic vertex, respectively. 16(a), (b), (c), respectively. The map geometry is gotten by endowing an angular function µ : V (M) → [0, 4π) on an embedding M for generalizing Iseri’s model 30 Chapter I Abstract Embeddings on surfaces following, which was first introduced in [Mao2]. , endow each vertex u, u ∈ V (M) with a real number µ(u), 0 < µ(u) < ρM4π(u) . The pair (M, µ) is called a map geometry without boundary, µ(u) an angle factor on u and orientable or non-orientable if M is orientable or not.

Endow each vertex u, u ∈ V (M) with a real number µ(u), 0 < µ(u) < ρM4π(u) . The pair (M, µ) is called a map geometry without boundary, µ(u) an angle factor on u and orientable or non-orientable if M is orientable or not. Map geometry with boundary Let (M, µ) be a map geometry without boundary, faces f1 , f2, · · · , fl ∈ F (M), 1 ≤ l ≤ φ(M) − 1. If S(M) \ {f1, f2, · · · , fl } is connected, then (M, µ)−l = (S(M) \ {f1, f2, · · · , fl }, µ) is called a map geometry with boundary f1, f2, · · · , fl , and orientable or not if (M, µ) is orientable or not, where S(M) denotes the underlying surface of M.

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Introductory Map Theory by Yanpei Liu


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