Knotting a 𝑘-connected closed 𝑃𝐿 𝑚-manifold in 𝐸^{2𝑚-𝑘}

Vrabec, Jože

doi:10.1090/S0002-9947-1977-0645405-0

Knotting a $k$-connected closed $\textrm {PL}$ $m$-manifold in $E^{2m-k}$
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by Jože Vrabec

Trans. Amer. Math. Soc. 233 (1977), 137-165

DOI: https://doi.org/10.1090/S0002-9947-1977-0645405-0

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Abstract:

Embeddings of a k-connected closed PL m-manifold $(0 \leqslant k \leqslant m - 3)$ in $(2m - k)$-dimensional euclidean space are classified up to isotopy. Thus this paper completes the results stated, and partly proved, in J. F. P. Hudson’s Piecewis linear topology.

References

Marvin J. Greenberg, Lectures on algebraic topology, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0215295
André Haefliger and Morris W. Hirsch, On the existence and classification of differentiable embeddings, Topology 2 (1963), 129–135. MR 149494, DOI 10.1016/0040-9383(63)90028-4
P. J. Hilton and S. Wylie, Homology theory: An introduction to algebraic topology, Cambridge University Press, New York, 1960. MR 0115161, DOI 10.1017/CBO9780511569289
J. F. P. Hudson, Knotted tori, Topology 2 (1963), 11–22. MR 146829, DOI 10.1016/0040-9383(63)90019-3
J. F. P. Hudson, Piecewise linear topology, W. A. Benjamin, Inc., New York-Amsterdam, 1969. University of Chicago Lecture Notes prepared with the assistance of J. L. Shaneson and J. Lees. MR 0248844
J. F. P. Hudson, Concordance, isotopy, and diffeotopy, Ann. of Math. (2) 91 (1970), 425–448. MR 259920, DOI 10.2307/1970632
R. Penrose, J. H. C. Whitehead, and E. C. Zeeman, Imbedding of manifolds in euclidean space, Ann. of Math. (2) 73 (1961), 613–623. MR 124909, DOI 10.2307/1970320
C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69, Springer-Verlag, New York-Heidelberg, 1972. MR 0350744, DOI 10.1007/978-3-642-81735-9
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
J. Vrabec, Isotopies of $\textrm {PL}$ manifolds keeping a subpolyhedron fixed, Glasnik Mat. Ser. III 11(31) (1976), no. 1, 141–154 (English, with Slovenian summary). MR 423360
C. T. C. Wall, Geometrical connectivity. I, J. London Math. Soc. (2) 3 (1971), 597–604. MR 290387, DOI 10.1112/jlms/s2-3.4.597
E. C. Zeeman, Isotopies and knots in manifolds, Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) Prentice-Hall, Englewood Cliffs, N.J., 1962, pp. 187–193. MR 0140097