Isotopy and homeomorphism
Author:
Dennis Kibler
Journal:
Proc. Amer. Math. Soc. 26 (1970), 499-502
MSC:
Primary 54.28; Secondary 55.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0266148-0
MathSciNet review:
0266148
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Abstract | References | Similar Articles | Additional Information
Abstract: If $X$ and $Y$ are isotopically equivalent topological spaces, they are not necessarily homeomorphic. If $X$ and $Y$ are compact without boundary manifolds or $n$-pure simplicial complexes, then isotopy equivalence implies topological equivalence. An example of compact manifolds with boundaries which are not homeomorphic but are isotopically equivalent is given.
- Daniel H. Gottlieb, Homotopy and isotopy properties of topological spaces, Canadian J. Math. 16 (1964), 561–571. MR 163311, DOI https://doi.org/10.4153/CJM-1964-057-x
- Sze-tsen Hu, Homotopy and isotopy properties of topological spaces, Canadian J. Math. 13 (1961), 167–176. MR 137118, DOI https://doi.org/10.4153/CJM-1961-013-9
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Keywords:
Isotopy equivalence,
<IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-pure simplicial complex,
stringless simplicial complex
Article copyright:
© Copyright 1970
American Mathematical Society