Constructing Seifert surfaces from n-bridge link projections

This paper presents a new algorithm "A" for constructing Seifert surfaces from n-bridge projections of links. The algorithm produces minimal complexity surfaces for large classes of braids and alternating links. In addition, we consider a family of knots for which the canonical genus is strictly greater than the genus, (g_c(K) > g(K)), and show that A builds surfaces realizing the knot genus g(K). We also present a generalization of Seifert's algorithm which may be used to construct surfaces representing arbitrary relative second homology classes in a link complement.Comment: 19 pages, 15 figure

Asymmetric hyperbolic L-spaces, Heegaard genus, and Dehn filling

An L-space is a rational homology 3-sphere with minimal Heegaard Floer homology. We give the first examples of hyperbolic L-spaces with no symmetries. In particular, unlike all previously known L-spaces, these manifolds are not double branched covers of links in S^3. We prove the existence of infinitely many such examples (in several distinct families) using a mix of hyperbolic geometry, Floer theory, and verified computer calculations. Of independent interest is our technique for using interval arithmetic to certify symmetry groups and non-existence of isometries of cusped hyperbolic 3-manifolds. In the process, we give examples of 1-cusped hyperbolic 3-manifolds of Heegaard genus 3 with two distinct lens space fillings. These are the first examples where multiple Dehn fillings drop the Heegaard genus by more than one, which answers a question of Gordon.Comment: 19 pages, 2 figures. v2: minor changes to intro. v3: accepted version, to appear in Math. Res. Letter

Dark Universe and distribution of Matter as Quantum Imprinting: the Quantum Origin of Universe

In this paper we analyze the Dark Matter problem and the distribution of matter through two different approaches, which are linked by the possibility that the solution of these astronomical puzzles should be sought in the quantum imprinting of the Universe. The first approach is based on a cosmological model formulated and developed in the last ten years by the first and third authors of this paper; the so-called Archaic Universe. The second approach was formulated by Rosen in 1933 by considering the Friedmann-Einstein equations as a simple one-dimensional dynamical system reducing the cosmological equations in terms of a Schroedinger equation. As an example, the quantum memory in cosmological dynamics could explain the apparently periodic structures of the Universe while Archaic Universe shows how the quantum phase concernts not only an ancient era of the Universe, but quantum facets permeating the entire Universe today.Comment: 18 page

Expression of cytokeratin 7 and 20 in pathological conditions of the bile tract

Expression of cytokeratin 7 (CK7) and cytokeratin 20 (CK20) helps to establish the origin of biliary and metastatic carcinomas. We investigated the expression of CK7 and CK20 in inflammatory, metaplastic and neoplastic conditions of the bile ducts, and evaluated possible relationships between the CK expression pattern and extrahepatic bile duct/gallbladder carcinomas (EBDCs) or intrahepatic bile duct carcinomas (IBDCs). We used immunohistochemistry for the investigation of 48 formalin-fixed, paraffin-embedded specimens grouped as: A) lithiasic or inflamed surgically resected extrahepatic bile ducts/gallbladders: all were CK7+/CK20+; B) percutaneous liver biopsies from patients with chronic hepatitis C primary biliary cirrhosis and primary sclerosing cholangitis: all were CK7+/CK20-; C) EBDCs: all were CK7+/CK20+, except for two cases which were CK7-/CK20-; D) IBDCs: all were CK7+/CK20-, except for one case showing CK20 positivity. Metaplastic changes were seen only among specimens in groups A and C: in these cases, CK20 was either focally or diffusely expressed. Our study suggests that the expression of cytokeratins under specific stimuli can be different from normal tissues, and that sometimes CK20 expression can be related to and precede the occurrence of metaplastic alterations