The curve complex has dead ends

Joan S. Birman; William W. Menasco

doi:10.1007/s10711-014-9978-y

The curve complex has dead ends

Joan S. Birman
, William W. Menasco

Mathematics

Columbia University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

It is proved that the curve graph (Formula presented.) of a surface (Formula presented.) g,n has a local pathology that had not been identified as such: there are vertices (Formula presented.) such that (Formula presented.) is a dead end of every geodesic joining (Formula presented.) to (Formula presented.). There are also double dead-ends. Every dead end has depth 1.

Original language	English
Pages (from-to)	71-74
Number of pages	4
Journal	Geometriae Dedicata
Volume	177
Issue number	1
DOIs	https://doi.org/10.1007/s10711-014-9978-y
State	Published - Aug 25 2015

Keywords

Curve complex
Dead end of a geodesic
Depth of a dead end

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10.1007/s10711-014-9978-y

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title = "The curve complex has dead ends",

abstract = "It is proved that the curve graph (Formula presented.) of a surface (Formula presented.) g,n has a local pathology that had not been identified as such: there are vertices (Formula presented.) such that (Formula presented.) is a dead end of every geodesic joining (Formula presented.) to (Formula presented.). There are also double dead-ends. Every dead end has depth 1.",

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AU - Menasco, William W.

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AB - It is proved that the curve graph (Formula presented.) of a surface (Formula presented.) g,n has a local pathology that had not been identified as such: there are vertices (Formula presented.) such that (Formula presented.) is a dead end of every geodesic joining (Formula presented.) to (Formula presented.). There are also double dead-ends. Every dead end has depth 1.

KW - Curve complex

KW - Dead end of a geodesic

KW - Depth of a dead end

UR - https://www.scopus.com/pages/publications/84937975032

U2 - 10.1007/s10711-014-9978-y

DO - 10.1007/s10711-014-9978-y

M3 - Article

AN - SCOPUS:84937975032

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VL - 177

SP - 71

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

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The curve complex has dead ends

Abstract

Keywords

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