2,631 research outputs found

    Cataloguing PL 4-manifolds by gem-complexity

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    We describe an algorithm to subdivide automatically a given set of PL n-manifolds (via coloured triangulations or, equivalently, via crystallizations) into classes whose elements are PL-homeomorphic. The algorithm, implemented in the case n=4, succeeds to solve completely the PL-homeomorphism problem among the catalogue of all closed connected PL 4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation with at most 18 4-simplices). Possible interactions with the (not completely known) relationship among different classification in TOP and DIFF=PL categories are also investigated. As a first consequence of the above PL classification, the non-existence of exotic PL 4-manifolds up to gem-complexity 8 is proved. Further applications of the tool are described, related to possible PL-recognition of different triangulations of the K3-surface.Comment: 25 pages, 5 figures. Improvements suggested by the refere

    Computing Matveev's complexity via crystallization theory: the boundary case

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    The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper we extend the definition to the case of non-empty boundary and prove that for each compact irreducible and boundary-irreducible 3-manifold it coincides with the modified Heegaard complexity introduced by Cattabriga, Mulazzani and Vesnin. Moreover, via Gem-Matveev complexity, we obtain an estimation of Matveev's complexity for all Seifert 3-manifolds with base D2\mathbb D^2 and two exceptional fibers and, therefore, for all torus knot complements.Comment: 27 pages, 14 figure

    Monoreactive high affinity and polyreactive low affinity rheumatoid factors are produced by CD5+ B cells from patients with rheumatoid arthritis.

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    In patients with rheumatoid arthritis (RA), circulating CD5+ B lymphocytes, but not CD5- B lymphocytes, are increased in number and size, exist in an activated state, spontaneously proliferate, and secrete Ig that binds to the Fc fragment of IgG. By constructing continuous mAb-secreting cell lines from CD5+ B lymphocytes, the properties and dissociation constants (Kd) of these antibodies were determined. Two types of rheumatoid factors (RFs) with discrete reactivities were produced. The first type is polyreactive and binds with relatively low affinity (Kd, 10(-5) mol/liter) to the Fc fragment of IgG. These antibodies are similar to those produced by CD5+ B cells from healthy subjects. The second type of RF is monoreactive and binds with higher affinity (Kd, 10(-7) mol/liter) to the Fc fragment of IgG. These latter autoantibodies are produced by CD5+ B cells of RA patients, but not healthy subjects. Long-term longitudinal studies are needed to determine the role of these two types of RFs in the pathogenesis of RA

    High Resolution Near-Infrared Spectra of Protostars

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    We present new high resolution (R = 21,000) near-infrared (2 microns) spectroscopic observations of a sample of Class I and flat-spectrum protostellar objects in the rho Ophiuchi dark cloud. None of the five Class I spectra show CO v = 0 -- 2 absorption features, consistent with high K-band continuum veilings, 4 <= r_k <= 20 and fast stellar rotation, assuming that the underlying protostellar photospheres are of late spectral type, as is suggested by the low luminosities of most of these objects. Two of the flat-spectrum protostellar objects also show no absorption features and are likely to be highly veiled. The remaining two flat-spectrum sources show weak, broad absorptions which are consistent with an origin in quickly rotating (v sin i ~ 50 km / s) late-type stellar photospheres which are also strongly veiled, r_k = 3 - 4. These observations provide further evidence that: 1)-Class I sources are highly veiled at near-infrared wavelengths, confirming previous findings of lower resolution spectroscopic studies; and 2)- flat-spectrum protostars rotate more rapidly than classical T Tauri stars (Class II sources), supporting findings from a recent high resolution spectroscopic study of other flat-spectrum sources in this cloud. In addition our observations are consistent with the high rotation rates derived for two of the Class I protostellar objects in our sample from observations of variable hard X-ray emission obtained with the ASCA satellite. These observations suggest that certain Class I sources can rotate even more rapidly than flat-spectrum protostars, near breakup velocity.Comment: 16 pages including 2 tables and 2 figures (AASTeX 5.x) to be published in The Astronomical Journal July 200

    Computing Matveev's complexity via crystallization theory: the orientable case

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    By means of a slight modification of the notion of GM-complexity introduced in [Casali, M.R., Topol. Its Appl., 144: 201-209, 2004], the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C-28 available in [Lins, S., Knots and Everything 5, World Scientific, Singapore, 1995] is used to obtain upper bounds for the complexity of closed orientable 3-manifolds triangulated by at most 28 tetrahedra. The experimental results actually coincide with the exact values of complexity, for all but three elements. Moreover, in the case of at most 26 tetrahedra, the exact value of the complexity is shown to be always directly computable via crystallization theory
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