By Danail Bonchev, Dennis H Rouvray

Topology has been greatly utilized within the research of chemically associated and knotted buildings, and in addition within the examine of many biologically major molecules resembling proteins and DNA. those are the topics which are addressed during this quantity of the Mathematical Chemistry sequence. The topological chirality of knotted and associated molecular species and the invariants which could represent them are explored intimately.

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Haltiwanger, J. Am. Chem. Soc. 104, 3219 (1982). 15. C. Kuratowski, Fund. Math. 15, 271 (1930). 16. J. Wilson, Introduction to Graph Theory, Academic Press, New York, 1979. 17. J. Simon, Topology 25, 229 (1986). 18. C. Millett in New Developments in Molecular Chirality (Ed. G. Mezey), Kluwer, Dordrecht, 1991, pp. 165-207. 19. C. Liang and K. Mislow, J. Math. Chem. 18, 1 (1995). 20. E. Wasserman, J. Am. Chem. Soc. 82, 4433 (1960). 21. G. Schill and A. Ltittringhaus, Angew. , Int. Ed. Engl. 3, 546 (1964).

Most of the time, chirality detectors are used to derive a property that serves as chirality specifier. Since no chirality detector is perfect, no classification scheme is perfect either: there always exist some chiral knots and links that cannot be classified in either class. Again, complete invari­ ants could be of help here, and might enable us to devise a perfect classi­ fication scheme. It has to be realized, however, that any classification scheme, even if it be perfect, is arbitrary. Two different perfect classi­ fication schemes could be imagined that lead to a different partition of knots and links.

Millett in New Developments in Molecular Chirality (Ed. G. Mezey), Kluwer, Dordrecht, 1991, pp. 165-207. 19. C. Liang and K. Mislow, J. Math. Chem. 18, 1 (1995). 20. E. Wasserman, J. Am. Chem. Soc. 82, 4433 (1960). 21. G. Schill and A. Ltittringhaus, Angew. , Int. Ed. Engl. 3, 546 (1964). 22. O. -P. Sauvage, Chem. Rev. 87, 795 (1987). 23. R. T. E. V. Z. Slawin, N. F. Stoddart, C. J. Williams, Angew. , Int. Ed. Engl. 28, 1396 (1989). 24. B. R. S. Reder, N. F. Stoddart, Angew. , Int. Ed. Engl. 33, 1286 (1994).

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Chemical Topology: Applications and Techniques by Danail Bonchev, Dennis H Rouvray
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