Formal $3$-deformations of $2$-polyhedra
HTML articles powered by AMS MathViewer
- by Perrin Wright
- Proc. Amer. Math. Soc. 37 (1973), 305-308
- DOI: https://doi.org/10.1090/S0002-9939-1973-0331397-2
- PDF | Request permission
Abstract:
A formal deformation of one polyhedron to another is a finite sequence of expansions and collapses, beginning with one polyhedron and ending with the other. If a formal deformation exists between two 2-dimensional polyhedra, it is possible to choose a deformation through polyhedra of dimension at most four. It is desired to reduce this number to three. We give a partial result in that direction.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
- B. G. Casler, An imbedding theorem for connected $3$-manifolds with boundary, Proc. Amer. Math. Soc. 16 (1965), 559–566. MR 178473, DOI 10.1090/S0002-9939-1965-0178473-0
- Hiroshi Ikeda, Acyclic fake surfaces, Topology 10 (1971), 9–36. MR 326735, DOI 10.1016/0040-9383(71)90013-9 C. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283.
- 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 J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939). 243-327.
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 305-308
- MSC: Primary 57C10; Secondary 57A10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0331397-2
- MathSciNet review: 0331397