A finite subdivision rule for the n-dimensional torus

Cannon, Floyd, and Parry have studied subdivisions of the 2-sphere extensively, especially those corresponding to 3-manifolds, in an attempt to prove Cannon's conjecture. There has been a recent interest in generalizing some of their tools, such as extremal length, to higher dimensions. We define finite subdivision rules of dimension n, and find an n-1-dimensional finite subdivision rule for the n-dimensional torus, using a well-known simplicial decomposition of the hypercube. We hope to expand on this and find finite subdivision rules for many higher-dimensional manifolds, including hyperbolic n-manifolds.Comment: Accepted by Geometriae Dedicata; ublished version available onlin

Cryptanalysis of group-based key agreement protocols using subgroup distance functions

We introduce a new approach for cryptanalysis of key agreement protocols based on noncommutative groups. This approach uses functions that estimate the distance of a group element to a given subgroup. We test it against the Shpilrain-Ushakov protocol, which is based on Thompson's group F

Surface finishing of intricate metal mould structures by large-area electron beam irradiation

The advancement of polymer moulding tools is increasingly focused on imparting not only form but also surface texture for functionality to the surfaces of parts that are created. Furthermore, the increasing demand for inexpensive and higher quality micro-components means that tools for replication processes must take advantage of advanced manufacturing techniques. Tools created by processes such as micro-investment casting, as in this case, may often suffer from excessive surface roughness, malformed edges and general deformation. This results in higher de-moulding forces and a reduction in fidelity of moulded parts to design intent. In this study, large-area electron beam irradiation (EB) is shown to be an effective technique for improving these metrics. For the first time, large population, high aspect ratio micro-features are subject to this process and the mechanisms of smoothing and key enhancement phenomena are demonstrated. The possibility of including EB irradiation in an integrated process chain for arriving at net shape is also discussed. Surfaces of protruding features are shown to have surface roughness reduced significantly from 126 to 22 nm Ra value, with bottom substrate also similarly improving from 150 to 27 nm Ra. Bottoms of recessed features are also observed to have much improved surface finishes. ‘Doming’ of tops of column features is also demonstrated, further enhancing form. These features would be far too fragile to be polished by any other mechanical method

The monoid of queue actions

We investigate the monoid of transformations that are induced by sequences of writing to and reading from a queue storage. We describe this monoid by means of a confluent and terminating semi-Thue system and study some of its basic algebraic properties, e.g., conjugacy. Moreover, we show that while several properties concerning its rational subsets are undecidable, their uniform membership problem is NL-complete. Furthermore, we present an algebraic characterization of this monoid's recognizable subsets. Finally, we prove that it is not Thurston-automatic

The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update

L^2-Betti numbers of one-relator groups

We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also obtain some information about the L^2-cohomology of left-orderable groups, and deduce the non-L^2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free.Comment: 18 pages, version 3, minor changes. To appear in Math. An

An infinite genus mapping class group and stable cohomology

We exhibit a finitely generated group \M whose rational homology is isomorphic to the rational stable homology of the mapping class group. It is defined as a mapping class group associated to a surface \su of infinite genus, and contains all the pure mapping class groups of compact surfaces of genus $g$ with $n$ boundary components, for any $g\geq 0$ and $n>0$. We construct a representation of \M into the restricted symplectic group ${\rm Sp_{res}}({\cal H}_r)$ of the real Hilbert space generated by the homology classes of non-separating circles on \su, which generalizes the classical symplectic representation of the mapping class groups. Moreover, we show that the first universal Chern class in H^2(\M,\Z) is the pull-back of the Pressley-Segal class on the restricted linear group ${\rm GL_{res}}({\cal H})$ via the inclusion ${\rm Sp_{res}}({\cal H}_r)\subset {\rm GL_{res}}({\cal H})$.Comment: 14p., 8 figures, to appear in Commun.Math.Phy

Hydrography and circulation near the crest of the East Pacific Rise between 9° and 10°N

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part I: Oceanographic Research Papers 58 (2011): 365-376, doi:10.1016/j.dsr.2011.01.009.Topography has a strong effect on the physical oceanography over the flanks and crests of the global mid-ocean ridge system. Here, we present an analysis of the hydrography and circulation near the crest of the East Pacific Rise (EPR) between 9◦ and 10◦N, which coincides with an integrated study site (ISS) of the RIDGE2000 program. The analysis is based primarily on survey and mooring data collected during the LADDER project, which aimed to investigate oceanographic and topographic influences on larval retention and dispersal in hydrothermal vent communities. Results indicate that the yearly averaged regional mean circulation is characterized by a westward drift of 0.5–1 cm·s−1 across the EPR axis and by north- and southward flows along the western and eastern upper ridge flanks, respectively. The westward drift is part of a basin-scale zonal flow that extends across most of the Pacific ocean near 10◦N, whereas the meridional currents near the ridge crest are a topographic effect. In spite of considerable mesoscale variability, which dominates the regional circulation and dispersal on weekly to monthly time scales, quasi-synoptic surveys carried out during the mooring deployment and recovery cruises indicate subinertial circulations that are qualitatively similar to the yearly averaged flow but associated with significantly stronger velocities. Weekly averaged mooring data indicate that the anticyclonically sheared along-flank flows are associated with core speeds as high as 10 cm·s−1 and extend ≈10 km off axis and 200m above the ridge-crest topography. Near the northern limit of the study region, the Lamont Seamount Chain rises from the western ridge flank and restricts along-EPR flow to five narrow passages, where peak velocities in excess of 20 cm·s−1 were observed. Outside the region of the ridge-crest boundary currents the density field over the EPR near 10◦N is characterized by isopycnals dipping into the ridge flanks. Directly above the EPR axis the ridge-crest boundary currents give rise to an isopycnal dome. During times of strong westward cross-EPR flow isopycnal uplift over the eastern flank causes the cross-ridge density field below the doming isopycnals to be asymmetric, with higher densities over the eastern than over the western flank. The data collected during the LADDER project indicate that dispersal of hydrothermal products from the EPR ISS on long time scales is predominantly to the west, whereas mesoscale variability dominates dispersal on weekly to monthly time scales, which are particularly important in the context of larval dispersal.Co-funding of the LADDER project by the biological and physical oceanography divisions of the National Science Foundation under grants OCE-0425361 and OCE-0424953 is gratefully acknowledged, as is support of J.W. Lavelle by NOAA’s Pacific Marine Environmental Laboratory and by the NOAA Vents Program

Finitely presented wreath products and double coset decompositions

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X^2. On the one hand, this extends a result of G. Baumslag about standard wreath products; on the other hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite topology.Comment: 21 pages; no figure. To appear in Geom. Dedicat

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for U \approx 2V in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential \Delta or bond alternation \delta. Although the alternating site potential \Delta strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation \delta destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with \delta contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of \Delta or \delta changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio