Betti numbers of finitely presented groups and very rapidly growing functions
نویسندگان
چکیده
منابع مشابه
Betti numbers of finitely presented groups and very rapidly growing functions
Define the length of a finite presentation of a group G as the sum of lengths of all relators plus the number of generators. How large can be the kth Betti number bk(G) = rank Hk(G) providing that G has length ≤ N and bk(G) is finite? We prove that for every k ≥ 3 the maximum bk(N) of kth Betti numbers of all such groups is an extremely rapidly growing function of N . It grows faster that all f...
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ژورنال
عنوان ژورنال: Topology
سال: 2007
ISSN: 0040-9383
DOI: 10.1016/j.top.2007.02.002