James B. Conant

Higher-order intersections in low-dimensional topology

We show how to measure the failure of the Whitney move in dimension 4 by constructing higher-order intersection invariants of Whitney towers built from iterated Whitney disks on immersed surfaces in 4-manifolds. For Whitney towers on immersed disks in the 4-ball, we identify some of these new invariants with previously known link invariants such as Milnor, Sato–Levine, and Arf invariants. We also define higher-order Sato–Levine and Arf invariants and show that these invariants detect the obstructions to framing a twisted Whitney tower. Together with Milnor invariants, these higher-order invariants are shown to classify the existence of (twisted) Whitney towers of increasing order in the 4-ball. A conjecture regarding the nontriviality of the higher-order Arf invariants is formulated, and related implications for filtrations of string links and 3-dimensional homology cylinders are described.

The Heat of Dissociation of the Carbon‐Carbon Linkage

Zieglers colorimetric measurements of the dissociation of hexaphenylethane provide information in regard to ΔF and ΔH for this process in solution. Assuming that ΔS for the dissociation of other similar compounds is approximately the same and independent of the temperature (over a short range), ΔF and ΔH of dissociation of a variety of compounds have been calculated from published data. It is suggested that the effects of substitution are approximately additive. There is evidence to indicate that the heat of activation of the association reaction of free radicals is very low; if this is the case the heats of dissociation estimated from the calculations of this paper provide information in regard to the heat of activation of the dissociation reaction.

Universal quadratic forms and Whitney tower intersection invariants

A general algebraic theory of quadratic forms is developed and then specialized from the non-commutative to the commutative to, finally, the symmetric settings. In each of these contexts we construct universal quadratic forms. We then show that the intersection invariant for twisted Whitney towers in the 4‐ball is such a universal symmetric refinement of the framed intersection invariant. As a corollary, we obtain a short exact sequence, Theorem 11, that has been essential in a sequence of papers by the authors on the classification of Whitney towers in the 4‐ball. 57N13; 11E16 Dedicated to Mike Freedman, on the occasion of his 60th birthday

A Truce Among Educators

mon, namely, intense ignorance of the present status and future problems of the public schools. Indeed, I imagine such ignorance is very widespread among educated people in the United States. I am almost tempted to generalize that the more educated the person, the less his knowledge of secondary-school education. Certainly the lack of knowledge among the professors of arts and sciences in our colleges and universities is proverbial. And with lack of information goes lack of understanding and lack of sympathy. As a result, on more than one campus we have almost a state of civil war between those who profess a knowledge of education and those who profess a knowledge of the wide range of subjects which constitute a modern educational curriculum. This academic war has been in a sense inevitable as I propose to show by a brief resume of history, but to my mind an armistice has been for some years overdue. And it is for such an armistice that I should like to put in a good word. (I might remark parenthetically that it takes two to make an armistice quite as much as to make a quarrel.) My belief in the need for the cessation

The Public High School and the National Interest

realize that, unless we cooperate, disaster may well face us as a nation. Gentlemen, this is true. I don’t believe that any generation has faced the responsibility that we face today. And, if that is true, you who shape, who mold this generation, who have them in your care as much as four and six hours a day have failed. I am sorry that I have to admit this, but the church too has failed, the home has failed. I’m not so sure that you have failed and I’m not just saying this because I want you to applaud. I believe that this nation, if it will look back and not panic as it first did when Sputnik streaked its ways across our skies, will realize that it is a nation that got the atom bomb up and down first, this nation which is looking for scientists also created radar, the kind that saved my life more than once, this nation has been able to delve in the universe and come up with more answers than I believe any other nation ever has. This nation is the one that came up with the wonder drugs; this nation is the one that came up with the Salk vaccine and, as long as that happens, gentlemen, we are not too far behind. But, at the

A report by the AEC General Advisory Committee

The Atomic Energy Act of 1946 provides in Section 2(b) that “There shall be a General Advisory Committee to advise the Commission on scientific and technical matters relating to materials, production, and research and development, to be composed of nine members, who shall be appointed from civilian life by the President.” The Act further directs that “The Committee shall designate one of its own members as Chairman. The Committee shall meet at least four times in every calendar year.” Beyond that, the Act does not specify how the Committee is to perform its advisory functions, how it is to obtain the information and analysis on which to base its advice, nor how to determine the issues to which it should direct its attention.

Cochran’s βi-invariants via twisted Whitney towers

We show that Tim Cochrans invariants

The Conway Polynomial and Amphicheiral Knots

\beta^i(L)

The Changing Educational Scene on Both Sides of the Atlantic

of a

The Unique Features of Our American Schools

2