The fundamental theorem of cubical small cancellation theory
Author:
Kasia Jankiewicz
Journal:
Trans. Amer. Math. Soc. 369 (2017), 4311-4346
MSC (2010):
Primary 20F65, 20F67
DOI:
https://doi.org/10.1090/tran/6852
Published electronically:
February 10, 2017
MathSciNet review:
3624411
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We give a new proof of the main theorem in the theory of 
small cancellation complexes. We prove the fundamental theorem of cubical small cancellation theory for 
cubical small cancellation complexes.
- [1] Martin Greendlinger, On Dehn’s algorithms for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641–677. MR 0125020, https://doi.org/10.1002/cpa.3160130406
- [2] Frédéric Haglund and Daniel T. Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008), no. 5, 1551–1620. MR 2377497, https://doi.org/10.1007/s00039-007-0629-4
- [3] Egbert R. Van Kampen, On Some Lemmas in the Theory of Groups, Amer. J. Math. 55 (1933), no. 1-4, 268–273. MR 1506963, https://doi.org/10.2307/2371129
- [4] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1977 edition. MR 1812024
- [5] Jonathan P. McCammond and Daniel T. Wise, Fans and ladders in small cancellation theory, Proc. London Math. Soc. (3) 84 (2002), no. 3, 599–644. MR 1888425, https://doi.org/10.1112/S0024611502013424
- [6]
Piotr Przytycki and Daniel T. Wise,
Mixed manifolds are virtually special,
http://arxiv.org/abs/1205.6742. - [7] V. A. Tartakovskiĭ, Solution of the word problem for groups with a 𝑘-reduced basis for 𝑘>6, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 483–494 (Russian). MR 0033816
- [8] Daniel T. Wise, Research announcement: the structure of groups with a quasiconvex hierarchy, Electron. Res. Announc. Math. Sci. 16 (2009), 44–55. MR 2558631, https://doi.org/10.3934/era.2009.16.44
- [9] D. T. Wise, Cubulating small cancellation groups, Geom. Funct. Anal. 14 (2004), no. 1, 150–214. MR 2053602, https://doi.org/10.1007/s00039-004-0454-y
- [10] Daniel T. Wise, From riches to raags: 3-manifolds, right-angled Artin groups, and cubical geometry, CBMS Regional Conference Series in Mathematics, vol. 117, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2012. MR 2986461
-reduced basis for 
, Izvestiya Akad. Nauk SSSR. Ser. Mat. 13 (1949), 483-494 (Russian). Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F65, 20F67
Retrieve articles in all journals with MSC (2010): 20F65, 20F67
Additional Information
Kasia Jankiewicz
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 0G4, Canada
Email:
kasia.jankiewicz@mcgill.ca
DOI:
https://doi.org/10.1090/tran/6852
Received by editor(s):
March 30, 2015
Received by editor(s) in revised form:
October 10, 2015
Published electronically:
February 10, 2017
Article copyright:
© Copyright 2017
American Mathematical Society
