Non-orientable surface-plus-one-relation groups

被引:4
作者
Antolin, Yago [1 ]
Dicks, Warren [1 ]
Linnell, Peter A. [2 ]
机构
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[2] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA
关键词
L-2-Betti number; Surface-plus-one-relation group; LOCALLY INDICABLE GROUPS; FREE-PRODUCTS; THEOREM; EQUATIONS; RING;
D O I
10.1016/j.jalgebra.2009.03.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Recently Dicks-Linnell determined the L-2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L-2-Betti numbers of the non-orientable surface-plus-one-relation groups. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码:4 / 33
页数:30
相关论文
共 27 条
[11]  
DICKS MJW, 1989, CAMBRIDGE STUD ADV M, V17
[12]   Retracts of vertex sets of trees and the almost stability theorem [J].
Dicks, Warren ;
Dunwoody, M. J. .
JOURNAL OF GROUP THEORY, 2007, 10 (05) :703-721
[13]   L2-Betti numbers of one-relator groups [J].
Dicks, Warren ;
Linnell, Peter A. .
MATHEMATISCHE ANNALEN, 2007, 337 (04) :855-874
[14]   ONE-RELATOR GROUPS HAVING ELEMENTS OF FINITE ORDER [J].
FISCHER, J ;
SOLITAR, D ;
KARRASS, A .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 33 (02) :297-&
[15]  
Gruenberg K.W., 1957, Proceedings of the London Mathematical Society, Vs3-7, P29, DOI [10.1112/plms/s3-7.1.29, /10.1112/plms/s3-7.1.29, DOI 10.1112/PLMS/S3-7.1.29]
[16]   ONE-RELATOR SURFACE GROUPS [J].
HEMPEL, J .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1990, 108 :467-474
[17]  
Howie J, 2004, BOL SOC MAT MEX, V10, P255
[18]   ON LOCALLY INDICABLE GROUPS [J].
HOWIE, J .
MATHEMATISCHE ZEITSCHRIFT, 1982, 180 (04) :445-461
[19]  
Howie J, 2000, PUBL MAT, V44, P641
[20]  
HOWIE J, 1981, J REINE ANGEW MATH, V324, P165