Geodesic
Homological filling functions with coefficients
Xingzhe Li1 ; Fedor Manin2
1University of California, Santa Barbara; Cornell University, Ithaca, USA
2University of California, Santa Barbara, USA
Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 889-907

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DOI

How hard is it to fill a loop in a Cayley graph with an unoriented surface? Following a comment of Gromov in “Asymptotic invariants of infinite groups”, we define homological filling functions of groups with coefficients in a group R. Our main theorem is that the coefficients make a difference. That is, for every n≥1 and every pair of coefficient groups A,B∈{Z,Q}∪{Z/pZ:p prime}, there is a group whose filling functions for n-cycles with coefficients in A and B have different asymptotic behavior.
DOI : 10.4171/ggd/675
Classification : 20-XX, 57-XX
Mots-clés : Homological filling functions, isoperimetric functions, Dehn functions, discrete Morse theory

Xingzhe Li  1   ; Fedor Manin  2

1 University of California, Santa Barbara; Cornell University, Ithaca, USA
2 University of California, Santa Barbara, USA 
Xingzhe Li; Fedor Manin. Homological filling functions with coefficients. Groups, geometry, and dynamics, Tome 16 (2022) no. 3, pp. 889-907. doi: 10.4171/ggd/675
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     year = {2022},
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     number = {3},
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