Filling radii of finitely presented groups
نویسندگان
چکیده
The filling radius function R of Gromov measures the minimal radii of van Kampen diagrams filling edge-circuits w in the Cayley 2complex of a finite presentation P. It is known that the Dehn function can be bounded above by a double exponential in R and the length of the loop, and it is an open question whether a single exponential bound suffices. We define the upper filling radius R(w) of w to be the maximal radius of minimal area fillings of w and let R be the corresponding filling function, so R(n) is the maximum of R(w) over all edge-circuits w of length at most n. We show that the Dehn function is bounded above by a single exponential in R and the length of the loop. We give an example of a finite presentation P where R is linearly bounded but R grows exponentially. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07
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