Peter J. Kahn

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Symplectic torus bundles ξ : T 2 → E → B are classified by the second cohomology group of B with local coefficients H1(T 2). For B a compact, orientable surface, the main theorem of this paper gives a necessary and sufficient condition on the cohomology class corresponding to ξ for E to admit a symplectic structure compatible with the symplectic bundle(More)
It has been known for almost 200 years that some angles cannot be trisected by straightedge and compass alone. This paper studies the set of such angles as well as its complement T , both regarded as subsets of the unit circle S 1. It is easy to show that both are topologically dense in S 1 and that T is contained in the countable set A of all angles whose(More)
The notion of a pseudocycle is introduced in [13] to provide a framework for defining Gromov-Witten invariants and quantum cohomology. This paper studies the bordism groups of pseu-docycles, called pseudohomology groups. These satisfy the Eilenberg-Steenrod axioms, and, for smooth compact manifold pairs, pseudohomology is naturally equivalent to homology.(More)
Pythagorean angles, that is angles with rational sines and cosines, provide an interesting environment for studying the question of characterizing trisectable angles. The main result of this paper shows that a Pythagorean angle is trisectable if and only if it is three times some other Pythagorean angle. Using the Euclidean parametrization of Pythagorean(More)
The eponymous theorem of P.L. Wantzel [Wan] presents a necessary and sufficient criterion for angle trisectability in terms of the third Chebyshev polynomial T3, thus making it easy to prove that there exist non-trisectable angles. We generalize this theorem to the case of all Chebyshev polynomials Tm (Corollary 1.4.1). We also study the set m-Sect(More)
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