The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
On the Structure of Manifolds
Abstract
In this paper, we prove a number of theorems which give some insight into the structure of differentiable manifolds. The methods, results and some notation of [13], hereafter referred to as GPC, and [12] will be used. These two papers and [14] can be considered as a starting point for this one. The main theorems in these papers are special cases of the theorems here. Among the most important theorems in this paper are 1. 1 and 6. 1. Some conversations with A. Haefliger were helpful in the preparation of parts of this paper. Everything will be considered from the differentable, equivalently C*, point of view; manifolds, imbeddings, and isotopes will be C*.
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Citations
Cites
Hirsch, M. W. (1959) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1959-0119214-4 · Cited by 491
Generalized Poincare's Conjecture in Dimensions Greater Than Four
Smale, S. (1961) · The Annals of Mathematics · doi:10.2307/1970239 · Cited by 428
Self-citationThe Self-Intersections of a Smooth n-Manifold in 2n-Space
Whitney, H. (1944) · Annals of Mathematics · doi:10.2307/1969265 · Cited by 403
Smale, S. (1961) · The Annals of Mathematics · doi:10.2307/1970311 · Cited by 396
Self-citation
Cited by
Kervaire, M. A., & Milnor, J. W. (1963) · The Annals of Mathematics · doi:10.2307/1970128 · Cited by 904
The Hamiltonian formalism and a many-valued analogue of Morse theory
Novikov, S. P. (1982) · Russian Mathematical Surveys · doi:10.1070/rm1982v037n05abeh004020 · Cited by 368
Classification problems in differential topology. V: On certain 6-manifolds
Wall, C. T. C. (1966) · Inventiones Mathematicae · doi:10.1007/bf01389738 · Cited by 292
Metadata
- Authors
- Smale, S.
- Venue
- American Journal of Mathematics
- Publisher
- JSTOR
- Published
- 1962-07
- Volume
- 84
- Issue
- 3
- Pages
- 387
- ISSN
- 0002-9327 (ISSN-L)
- OpenAlex
- W2092637653
- Cited by
- 379
- References
- 4
- FWCI
- 21.50
- Type
- journal article
- Language
- en
- Open access
- closed
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