We give a new proof of the theorem of Krstić–McCool from the title. Our proof has potential applications to the study of finiteness properties of other subgroups of SL2 resulting from rings of functions on curves.
Bux, Kai-Uwe  1 ; Wortman, Kevin  2
@article{10_2140_agt_2006_6_839,
author = {Bux, Kai-Uwe and Wortman, Kevin},
title = {A geometric proof that {SL2(\ensuremath{\mathbb{Z}}[t,t\ensuremath{-}1])} is not finitely presented},
journal = {Algebraic and Geometric Topology},
pages = {839--852},
year = {2006},
volume = {6},
number = {2},
doi = {10.2140/agt.2006.6.839},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.839/}
}
TY - JOUR AU - Bux, Kai-Uwe AU - Wortman, Kevin TI - A geometric proof that SL2(ℤ[t,t−1]) is not finitely presented JO - Algebraic and Geometric Topology PY - 2006 SP - 839 EP - 852 VL - 6 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2006.6.839/ DO - 10.2140/agt.2006.6.839 ID - 10_2140_agt_2006_6_839 ER -
Bux, Kai-Uwe; Wortman, Kevin. A geometric proof that SL2(ℤ[t,t−1]) is not finitely presented. Algebraic and Geometric Topology, Tome 6 (2006) no. 2, pp. 839-852. doi: 10.2140/agt.2006.6.839
[1] , , Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445
[2] , , Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436
[3] , Finiteness properties of groups, J. Pure Appl. Algebra 44 (1987) 45
[4] , , Finiteness properties of arithmetic groups over function fields, Invent. Math. (to appear)
[5] , , The non-finite presentability of IA(F3) and GL2(Z[t,t−1]), Invent. Math. 129 (1997) 595
[6] , , Presenting GLn(k⟨T⟩), J. Pure Appl. Algebra 141 (1999) 175
[7] , Trees, Springer (1980)
[8] , Homological properties of certain arithmetic groups in the function field case, Invent. Math. 57 (1980) 263
[9] , The structure of the special linear group over rings of polynomials, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977) 235, 477
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