This paper introduces the concept of a topological rubber glove and gives several examples. In particular, we prove that the knot 817 and the molecular graph of a single stranded DNA figure eight knot are topological rubber gloves. Then, we present an embedded graph which is not only a topological rubber glove, but has the additional property that no embedding of the graph can be rotated to its mirror image
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
J.-C. Chambron, J.-P. Sauvage and K. Mislow, A chemically achiral molecule with no rigid achiral presentations, J. Am. Chem. Soc. (1997) 9558–9559.
S. Du and N. Seeman, Synthesis of a DNA knot containing both positive and negative nodes, J. Am. Chem. Soc. 114 (1992) 9652–9655.
E. Flapan, Rigid and non-rigid achirality, Pacific J. Math. 129 (1987) 57–66.
E. Flapan, Symmetries of Möbius ladders, Math. Ann. 283 (1989) 271–283.
E. Flapan, Rigid and flexible symmetries of embedded graphs, New J. Chem. 17 (1993) 645–653.
E. Flapan and N. Seeman, A topological rubber glove obtained from a synthetic single-stranded DNA molecule, J. Chem. Soc. Chem. Comm. (1995) 2249–2250.
N. van Gulick, Theoretical aspects of the linked ring problem, New J. Chem. 17 (1993) 619–625.
A. Kawauchi, The invertibility problem on amphicheiral excellent knots, Proc. Japan Acad. Series A 55 (1979) 399–402.
K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930) 271–283.
C. Liang and K. Mislow, Topological features in proteins: knots and links, J. Am. Chem. Soc. 117 (1995) 4201–4213.
K. Mislow, Limitations of the symmetry criteria for optical inactivity and resolvability, Science 120 (1954) 232–233.
K. Mislow and R. Bolstad, Molecular dissymetry and optical inactivity, J. Am. Chem. Soc. 77 (1955) 6712–6713.
D. Rolfsen, Knots and Links (Publish or Perish Press, Berkeley, 1976).
J. Simon, Topological chirality of certain molecules, Topology 25 (1986) 229–235.
P.A. Smith, Transformations of finite period II, Ann. Math. 40 (1939) 690–711.
D. Walba, Stereochemical topology, in: Chemical Applications of Topology and Graph Theory, ed. R.B. King, Studies in Physical and Theoretical Chemistry, Vol. 28 (Elsevier, Amsterdam, 1983) pp. 17–32.
D. Walba, Molecular chirality and other tidbits in stereochemistry, in: New Developments in Molecular Chirality, ed. P.G. Mezey (Kluwer, Dordrecht, 1991) pp. 119–129.
D. Walba, J. Armstrong, A. Perry, R. Richards, T. Homan and R. Haltiwanger, The thyme polyethers. An approach to the synthesis of a molecular knotted ring, Tetrahedron 42 (1986) 1883–1894.
D. Walba, R. Richards and R.C. Haltiwanger, Total synthesis of the first molecular Möbius strip, J. Am. Chem. Soc. 104 (1982) 3219–3221.