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Spines and Embeddings of n ‐Manifolds
Author(s) -
Matveev Sergei,
Rolfsen Dale
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799006973
Subject(s) - cartesian product , codimension , product (mathematics) , spine (molecular biology) , manifold (fluid mechanics) , interval (graph theory) , mathematics , cartesian coordinate system , combinatorics , pure mathematics , physics , geometry , engineering , biology , bioinformatics , mechanical engineering
Every compact, connected PL manifold M n , with ∂ M n ≠Ø, collapses to a codimension‐one subpolyhedron Q n −1 , called a spine of M n . The purpose of this paper is to prove that, if Q n −1 is appropriately chosen, one can reconstruct M n from Q n −1 , after taking the Cartesian product with an interval I =[0, 1].