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New York Journal of Mathematics
Volume 27 (2021), 881-902

  

Ursula Hamenstädt

Spotted disk and sphere graphs I

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Published: June 8, 2021.
Keywords: Disk graphs, handlebodies with spots, embedded flats, sphere graphs.
Subject: 57M99.

Abstract
The disk graph of a handlebody H of genus g ≥ 2 with m ≥ 0 marked points on the boundary is the graph whose vertices are isotopy classes of disks disjoint from the marked points and where two vertices are connected by an edge of length one if they can be realized disjointly. We show that for m=1 the disk graph contains quasi-isometrically embedded copies of R2. The same holds true for sphere graphs of the doubled handlebody with one marked points provided that g is even.

Acknowledgements

Partially supported by ERC Grant "Moduli''.


Author information

Ursula Hamenstädt:
MATH. INSTITUT DER UNIVERSITÄT BONN
ENDENICHER ALLEE 60
53115 BONN, GERMANY

ursula@math.uni-bonn.de