The classification of two-dimensional manifolds
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- by Edward M. Brown and Robert Messer PDF
- Trans. Amer. Math. Soc. 255 (1979), 377-402 Request permission
Abstract:
Invariants are constructed to classify all noncompact 2-manifolds including those with boundary. The invariants of a 2-manifold M are the space of ends of M and the subspaces of nonplanar ends, of nonorientable ends, and of ends that are limits of compact boundary components. Also the space of ends of the boundary components together with its natural map into the ends of M and the orientation of these ends induced by orientations of neighborhoods of the orientable ends of M are used in addition to the usual compact invariants. Special properties are established for the invariants of a 2-manifold, and a 2-manifold is constructed for each set of invariants with the special properties.References
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Magarida Barros, Classification of non-compact surfaces whose boundary is the union of Jordan curves, An. Fac. Ci. Univ. Porto. 57 (1974), 33-41.
- E. M. Brown and T. W. Tucker, On proper homotopy theory for noncompact $3$-manifolds, Trans. Amer. Math. Soc. 188 (1974), 105–126. MR 334225, DOI 10.1090/S0002-9947-1974-0334225-X
- Martin E. Goldman, An algebraic classification of noncompact $2$-manifolds, Trans. Amer. Math. Soc. 156 (1971), 241–258. MR 275436, DOI 10.1090/S0002-9947-1971-0275436-9 B. Kerékjártó, Vorlesungen über Topologie, Vol. I, Springer, Berlin, 1923.
- Ian Richards, On the classification of noncompact surfaces, Trans. Amer. Math. Soc. 106 (1963), 259–269. MR 143186, DOI 10.1090/S0002-9947-1963-0143186-0
- Richard J. Tondra, Homeotopy groups of surfaces whose boundary is the union of $1$-spheres, Fund. Math. 105 (1979/80), no. 2, 79–85. MR 561583, DOI 10.4064/fm-105-2-79-85
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 255 (1979), 377-402
- MSC: Primary 57N05; Secondary 57M20
- DOI: https://doi.org/10.1090/S0002-9947-1979-0542887-1
- MathSciNet review: 542887