 

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 quasiisometrically embedded copies of R^{2}.
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.unibonn.de

