Group presentations and formal deformations

Wright, Perrin

doi:10.1090/S0002-9947-1975-0380813-5

Group presentations and formal deformations
HTML articles powered by AMS MathViewer

by Perrin Wright PDF

Trans. Amer. Math. Soc. 208 (1975), 161-169 Request permission

Abstract:

Formal deformations (expansions and collapses) of dimension $\leqslant 3$ among $2$-dimensional polyhedra are explained in terms of a certain collection of operations on finite group presentations. The results are valid for any simple homotopy type of $2$-dimensional polyhedra, and simplifications are possible within the simply connected simple homotopy types.

References

J. J. Andrews and M. L. Curtis, Free groups and handlebodies, Proc. Amer. Math. Soc. 16 (1965), 192–195. MR 173241, DOI 10.1090/S0002-9939-1965-0173241-8
D. R. J. Chillingworth, Collapsing three-dimensional convex polyhedra, Proc. Cambridge Philos. Soc. 63 (1967), 353–357. MR 210100, DOI 10.1017/s0305004100041268
H. F. Trotter, Homology of group systems with applications to knot theory, Ann. of Math. (2) 76 (1962), 464–498. MR 143201, DOI 10.2307/1970369
C. T. C. Wall, Formal deformations, Proc. London Math. Soc. (3) 16 (1966), 342–352. MR 193635, DOI 10.1112/plms/s3-16.1.342

Simplicial spaces, nuclei, and $m$-groups

45

J. H. C. Whitehead, On incidence matrices, nuclei and homotopy types, Ann. of Math. (2) 42 (1941), 1197–1239. MR 5352, DOI 10.2307/1970465