Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to the boundary, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M,v,L), with (M,v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v and isotopy of L). All realizations are based on the notion of branched standard spine, and build on results previously obtained. Links are encoded by means of diagrams on branched spines, where the diagram is smooth with respect to the branching. Several motivations for being interested in combinatorial realizations of the topological categories considered in this paper are given in the introduction. The encoding of links is suitable for the comparison of the framed and the pseudo-Legendrian categories, and some applications are given in connection with contact structures, torsion and finite-order invariants. An estension of Trace's notion of winding number of a knot diagram is introduced and discussed.Comment: 38 pages, 33 figure

A new invariant on hyperbolic Dehn surgery space

In this paper we define a new invariant of the incomplete hyperbolic structures on a 1-cusped finite volume hyperbolic 3-manifold M, called the ortholength invariant. We show that away from a (possibly empty) subvariety of excluded values this invariant both locally parameterises equivalence classes of hyperbolic structures and is a complete invariant of the Dehn fillings of M which admit a hyperbolic structure. We also give an explicit formula for the ortholength invariant in terms of the traces of the holonomies of certain loops in M. Conjecturally this new invariant is intimately related to the boundary of the hyperbolic Dehn surgery space of M.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-23.abs.htm

Complexity of links in 3-manifolds

We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a closed orientable 3-manifold and L is a link contained in M. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal number of tetrahedra in a triangulation of M containing L in its 1-skeleton. Slightly adapting Matveev's recent theory of roots for graphs, we carefully analyze the behaviour of c under connected sum away from and along the link. We show in particular that c is almost always additive, describing in detail the circumstances under which it is not. To do so we introduce a certain (0,2)-root for a pair X, we show that it is well-defined, and we prove that X has the same complexity as its (0,2)-root. We then consider, for links in the 3-sphere, the relations of c with the crossing number and with the hyperbolic volume of the exterior, establishing various upper and lower bounds. We also specialize our analysis to certain infinite families of links, providing rather accurate asymptotic estimates.Comment: 24 pages, 6 figure

Efficacy and microbiota modulation induced by limpial 2.5%, a new medical device for the inverse psoriasis treatment

(1) Inverse psoriasis (IP), also known as intertriginous, typically affects the groin, armpits, navel, intergluteal fissure, and external genitalia. Skin lesions are erythematous plaques of inflammatory nature, smooth, well-delimited, non-scaly, and non-infiltrated. Lesions may be accompanied by itching, pain, or burning sensation. The aim of this study is both to investigate the modulation of the skin microbiota induced by IP and, on the other hand, to test the effectiveness of the new biotechnological product LimpiAL 2.5%. (2) Patients affected by IP were recruited in a private practice and treated for 4 weeks with LimpiAL 2.5% exclusively. The clinical effects on the lesion skin were evaluated, and the skin microbiotas before and after treatment were compared. (3) The clinical outcomes reveled a significant beneficial effect of the tested product. At the same time, LimpiAL increased the biological diversity of the skin microbiota and exerted a significant decrease of some Corynebacterium species, and the increase of some Staphylococcus species. (4) Together, the clinical outcomes and the microbiota analysis suggest that LimpiAL treatment improves the skin condition of affected patients, basically restoring the eubiosis conditions of the affected sites and modulating the bacterial composition of the resident microbiota

Noncyclic covers of knot complements

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\Phi (c)$ sheets.Comment: 29 pages, 8 figures, from Ph.D. thesis at Columbia University; Acknowledgments added; Content correcte

Sub-Nyquist Field Trial Using Time Frequency Packed DP-QPSK Super-Channel Within Fixed ITU-T Grid

Sub-Nyquist time frequency packing technique was demonstrated for the first time in a super channel field trial transmission over long-haul distances. The technique allows a limited spectral occupancy even with low order modulation formats. The transmission was successfully performed on a deployed Australian link between Sydney and Melbourne which included 995 km of uncompensated SMF with coexistent traffic. 40 and 100 Gb/s co-propagating channels were transmitted together with the super-channel in a 50 GHz ITU-T grid without additional penalty. The super-channel consisted of eight sub-channels with low-level modulation format, i.e. DP-QPSK, guaranteeing better OSNR robustness and reduced complexity with respect to higher order formats. At the receiver side, coherent detection was used together with iterative maximum-a-posteriori (MAP) detection and decoding. A 975 Gb/s DP-QPSK super-channel was successfully transmitted between Sydney and Melbourne within four 50GHz WSS channels (200 GHz). A maximum potential SE of 5.58 bit/s/Hz was achieved with an OSNR=15.8 dB, comparable to the OSNR of the installed 100 Gb/s channels. The system reliability was proven through long term measurements. In addition, by closing the link in a loop back configuration, a potential SE*d product of 9254 bit/s/Hz*km was achieved

Pequeños vertebrados del relleno kárstico del Pleistoceno Superior de Avetrana (Apulia, Sur de Italia)

The fossiliferous deposit (karst cavity) in La Grave, a locality near the small town of Avetrana (Taranto, south­ern Italy), has yielded numerous fossils of vertebrates. The remains of large mammals have been the subject of several studies. This paper examines the remains of small vertebrates and identifies four taxa of amphibians (Bufo bufo, Bufotes gr. B. viridis, Hyla gr. H. Arborea and Rana (s.l.) sp.), four taxa of reptiles (Testudo hermanni, Podarcis sp., Zamenis gr. Z. longissimus, Natrix natrix), and nine taxa of small mammals (Erinaceus europaeus, Crocidura suaveolens, Arvicola italicus, Microtus (Terricola) savii, Microtus (Microtus) arvalis, Apodemus gr. A. sylvaticus - A. flavicollis, Hystrix (Acanthion) vinogradovi, Oryctolagus cuniculus and Lepus corsicanus). From a biochronological point of view, the data on small and large vertebrates indicate an age between the beginning of the Late Pleistocene (MIS 5e) and the central part of MIS 3. The most recent fossiliferous layer (bed 8) is likely to have been deposited during a cooler period when compared to the previous layers.The data from small fossil vertebrates combined with those emerging from the large mammals and birds evidence the presence, near the karstic cavity, of open spaces (prairies) with pools of water, bordered by wooded areas and, not far, the presence of a rocky coastline.El depósito (cavidad kárstica) de La Grave, localidad cercana a la pequeña ciudad de Avetrana (Tarento, Italia meridional), ha dado lugar a numerosos fósiles de vertebrados. Los restos de grandes mamíferos han sido objeto de varios estudios. En este trabajo se examinan los restos de pequeños vertebrados y se identifican cuatro taxones de anfibios (Bufo bufo, Bufotes gr. B. viridis, Hyla gr. H. Arborea and Rana (s.l.) sp.), cuatro de reptiles (Testudo hermanni, Podarcis sp., Zamenis gr. Z. longissimus, Natrix natrix), y nueve de pequeños mamíferos (Erinaceus europaeus, Crocidura suaveolens, Arvicola italicus, Microtus (Terricola) savii, Microtus (Microtus) arva­lis, Apodemus gr. A. sylvaticus - A. flavicollis, Hystrix (Acanthion) vinogradovi, Oryctolagus cuniculus and Lepus corsicanus). Desde un punto de vista biocronológico, los datos sobre los vertebrados pequeños y grandes indican una edad entre el comienzo del Pleistoceno tardío (MIS 5e) y la parte central del MIS 3. Es probable que el estrato fosilífero más reciente (nivel 8) se haya depositado durante un período más frío en comparación con las capas anteriores. Los datos de pequeños vertebrados fósiles combinados con los que proceden de los grandes mamífe­ros y aves evidencian la presencia, cerca de la cavidad kárstica, de espacios abiertos (praderas) con charcos de agua, bordeados por zonas boscosas y, no muy lejos, la presencia de una costa rocosa