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Through numerous conversations with other synthetic chemists it became apparent that the great power of carbon nuclear magnetic resonance was being significantly underutilized. In our own work we have found that 13C spectroscopy is a more powerful tool than IH NMR spectroscopy, especially for probing subtle stereochemical questions in complicated systems. This is especially true in five membered ring compounds where IH NMR is at a particular disadvantage. The two techniques can be used independently to solve the same question-that of stereochemistry - but they do so in different ways. Advantage can be taken in IH NMR of a relatively consistent relationship between stereochemical orientation and coupling constants between vicinal protons, while in 13C NMR it is the correlation between spatial relationships of non-hydrogen, y substituents and their effect on chemical shift that can be used to assign stereochemistry. It was also clear that the use of 13C NMR required a different approach to problem solving than that typically used with IH NMR. While the latter technique could be employed with a very general approach (e.g., the Karplus equation), 13C NMR would, at least for the immediate future, require a relatively extensive set of model systems from which the consequences of stereochemical changes could be derived for any given carbon framework.

This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.

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