Cyclic group actions and embedded spheres in 4-manifolds

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is given by one half of the Euler characteristic of the 4-manifold. The result also shows that in some cases the 4-manifold does not admit such actions of a certain order at all or that any such action has to be pseudofree.Comment: 13 pages; to appear in Proc. Amer. Math. So

Minimality and irreducibility of symplectic four-manifolds

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of holomorphic minimality for complex surfaces with even first Betti number which are not Hirzebruch surfaces.Comment: final version; cosmetic changes only; to appear in International Mathematics Research Notice

Iterated fibre sums of algebraic Lefschetz fibrations

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz pencil on a simply-connected minimal surface of general type we partially calculate the Seiberg-Witten invariants of the fibre sum M(n) using a formula of Morgan-Szabo-Taubes. As an application we derive an obstruction for self-diffeomorphisms of the boundary of the tubular neighbourhood of a general fibre in M(n) to extend over the complement of the neighbourhood. Similar obstructions are known in the case of elliptic surfaces.Comment: 14 pages; to appear in Quart. J. Mat

Isobar-free neon isotope measurements of flux-fused potential reference minerals on a Helix-MC-Plus^(10K) mass spectrometer

This work presents new analytical techniques for extraction and analysis of neon from a suite of different mineral phases, including quartz, pyroxene, hematite, apatite, zircon, topaz, and fluorite. Neon was quantitatively extracted at 1100 °C from all of these minerals using an in-vacuum lithium borate-flux fusion technique. Evolved neon was purified using a cryogenic method capable of separating Ne from He present in abundances ~8 orders of magnitude higher, typical of samples carrying nucleogenic/radiogenic noble gases. The purified neon was measured on a Helix-MC-Plus^(10K) mass spectrometer that permits isobar-free measurement of all three neon isotopes. When operated at its highest mass resolving power (MRP) of ~10,300, the shoulder representing solely ²²Ne on the low mass-side of the ²²Ne-CO₂⁺² doublet is wide enough to permit measurement of isobar free ²²Ne. Operating in this mode comes with the penalty of a 50% reduction in neon sensitivity. Coupled with a mathematical isobar-stripping method, this approach excludes 99.5% of the CO₂⁺² while still collecting >99% of the ²²Ne beam. Routine edge-centering on the dynamic CO₂⁺² peak prior to introduction of a sample permits rapid and robust relocation of the desired measure point in the mass spectrum. Cosmogenic ²¹Ne and ²²Ne concentrations obtained using these methods on the Cronus-A quartz and Cronus-P pyroxene international reference materials are in excellent agreement with previous work or expectations. Similarly, the concentration of nucleogenic ²¹Ne and ²²Ne in Durango apatite and the CIT hematite standard agree well with previous work. Durango apatite has notable heterogeneity in neon concentrations, consistent with previous observations of heterogeneous He, U and Th concentrations in this apatite. Nucleogenic neon concentrations are also presented for previously unstudied minerals including a Sri Lanka zircon (SLC), a topaz from the Imperial Topaz mine in Brazil (ITP1), and a fluorite (W-90) from New Hampshire. Taken together this set of potential reference minerals and the associated dataset provide a starting point for intercalibration among multiple mineral phases carrying ²¹Ne and ²²Ne of cosmogenic or nucleogenic origin