Premium
Nilpotent groups without exactly polynomial Dehn function
Author(s) -
Wenger Stefan
Publication year - 2011
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jtq038
Subject(s) - mathematics , nilpotent , nilpotent group , class (philosophy) , function (biology) , pure mathematics , polynomial , group (periodic table) , finitely generated abelian group , quadratic equation , dehn surgery , combinatorics , central series , discrete mathematics , mathematical analysis , geometry , computer science , chemistry , organic chemistry , artificial intelligence , evolutionary biology , chemical engineering , knot (papermaking) , engineering , biology
We prove super‐quadratic lower bounds for the growth of the filling area function of a certain class of nilpotent Lie groups. This class contains groups for which it is known that their Dehn function grows no faster than n 2 log n . We therefore obtain the existence of (finitely generated) nilpotent groups whose Dehn functions do not have exactly polynomial growth and we thus answer a well‐known question about the possible growth rate of Dehn functions of nilpotent groups.