Simplexwise linear near-embeddings of a -disk into

Author:
Ethan D. Bloch

Journal:
Trans. Amer. Math. Soc. **288** (1985), 701-722

MSC:
Primary 57N05; Secondary 03H99, 57N35, 57Q99

DOI:
https://doi.org/10.1090/S0002-9947-1985-0776399-X

MathSciNet review:
776399

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finitely triangulated -disk; a map is called *simplexwise linear* if is affine linear for each (closed) simplex of . Interest in maps originated with work of S. S. Cairns and subsequent work of R. Thom and N. H. Kuiper. Let , , and denote their respective closures in the space of all maps and the space of all maps fixing . The main result of this paper is useful characterizations of maps in and some maps in , including the relation of such maps to embeddings into the nonstandard plane.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0776399-X

Keywords:
Simplexwise linear,
spaces of embeddings,
nonstandard plane

Article copyright:
© Copyright 1985
American Mathematical Society