TY - JOUR
T1 - Homological and homotopical Dehn functions are different
AU - Abrams, Aaron
AU - Brady, Noel
AU - Dani, Pallavi
AU - Young, Robert
PY - 2013/11/26
Y1 - 2013/11/26
N2 - The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, whereas the homotopical Dehn function measures fillings of curves by disks. Because the two definitions involve different sorts of boundaries and fillings, there is no a priori relationship between the two functions; however, before this work, there were no known examples of finitely presented groups for which the two functions differ. This paper gives such examples, constructed by amalgamating a free-by-cyclic group with several Bestvina-Brady groups.
AB - The homological and homotopical Dehn functions are different ways of measuring the difficulty of filling a closed curve inside a group or a space. The homological Dehn function measures fillings of cycles by chains, whereas the homotopical Dehn function measures fillings of curves by disks. Because the two definitions involve different sorts of boundaries and fillings, there is no a priori relationship between the two functions; however, before this work, there were no known examples of finitely presented groups for which the two functions differ. This paper gives such examples, constructed by amalgamating a free-by-cyclic group with several Bestvina-Brady groups.
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U2 - 10.1073/pnas.1207377110
DO - 10.1073/pnas.1207377110
M3 - Article
C2 - 23908405
AN - SCOPUS:84888325045
SN - 0027-8424
VL - 110
SP - 19206
EP - 19212
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 48
ER -