Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On embedding polyhedra and manifolds

Author: Krešo Horvatić
Journal: Trans. Amer. Math. Soc. 157 (1971), 417-436
MSC: Primary 57.01
MathSciNet review: 0278314
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that every $ n$-polyhedron PL embeds in a Euclidean $ (2n + 1)$-space, and that for PL manifolds the result can be improved upon by one dimension. In the paper are given some sufficient conditions under which the dimension of the ambient space can be decreased. The main theorem asserts that, for there to exist an embedding of the $ n$-polyhedron $ X$ into $ 2n$-space, it suffices that the integral cohomology group $ {H^n}(X - \operatorname{Int} A) = 0$ for some $ n$-simplex $ A$ of a triangulation of $ X$. A number of interesting corollaries follow from this theorem. Along the line of manifolds the known embedding results for PL manifolds are extended over a larger class containing various kinds of generalized manifolds, such as triangulated manifolds, polyhedral homology manifolds, pseudomanifolds and manifolds with singular boundary. Finally, a notion of strong embeddability is introduced which allows us to prove that some class of $ n$-manifolds can be embedded into a $ (2n - 1)$-dimensional ambient space.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57.01

Retrieve articles in all journals with MSC: 57.01

Additional Information

PII: S 0002-9947(1971)0278314-4
Keywords: PL category, PL embeddings, polyhedra, PL manifolds, generalizations of manifolds, strong embeddability
Article copyright: © Copyright 1971 American Mathematical Society