An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants

We prove an analogue of the Kotschick-Morgan conjecture in the context of SO(3) monopoles, obtaining a formula relating the Donaldson and Seiberg-Witten invariants of smooth four-manifolds using the SO(3)-monopole cobordism. The main technical difficulty in the SO(3)-monopole program relating the Seiberg-Witten and Donaldson invariants has been to compute intersection pairings on links of strata of reducible SO(3) monopoles, namely the moduli spaces of Seiberg-Witten monopoles lying in lower-level strata of the Uhlenbeck compactification of the moduli space of SO(3) monopoles [arXiv:dg-ga/9710032]. In this monograph, we prove --- modulo a gluing theorem which is an extension of our earlier work in [arXiv:math/9907107] --- that these intersection pairings can be expressed in terms of topological data and Seiberg-Witten invariants of the four-manifold. This conclusion is analogous to the Kotschick-Morgan conjecture concerning the wall-crossing formula for Donaldson invariants of a four-manifold with $b_2^+=1$; that wall-crossing formula and the resulting structure of Donaldson invariants for four-manifolds with $b_2^+=1$ were established, assuming the Kotschick-Morgan conjecture, by Goettsche [arXiv:alg-geom/9506018] and Goettsche and Zagier [arXiv:alg-geom/9612020]. In this monograph, we reduce the proof of the Kotschick-Morgan conjecture to an extension of previously established gluing theorems for anti-self-dual SO(3) connections (see [arXiv:math/9812060] and references therein). Since the first version of our monograph was circulated, applications of our results have appeared in the proof of Property P for knots by Kronheimer and Mrowka [arXiv:math/0311489] and work of Sivek on Donaldson invariants for symplectic four-manifolds [arXiv:1301.0377].Comment: x + 229 page

Dungeness crab research program

In 1974, the California State Legislature, recognizing the problem of low yields from the Dungeness crab resource of central California, directed the Department of Fish and Game to conduct an investigation into the causes of the decline. The Operations Research Branch of the Department has conducted preliminary studies and field operations necessary to formulate the Dungeness Crab Research Program. The objectives, research design, and work plans are presented for a 4-year program from July 1, 1975 through August 31, 1979. (38pp.

Ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV above threshold

We present here triple differential cross sections for ionization of hydrogen atoms by electron impact at 1eV, 0.5eV and 0.3eV energy above threshold, calculated in the hyperspherical partial wave theory. The results are in very good agreement with the available semiclassical results of Deb and Crothers \cite{DC02} for these energies. With this, we are able to demonstrate that the hyperspherical partial wave theory yields good cross sections from 30 eV \cite{DPC03} down to near threshold for equal energy sharing kinematics.Comment: 6 pages, 9 figure