1,720,990 research outputs found
Exceptional surgeries on certain (1,1)-knots
Get PDFWe determine certain exceptional surgeries on a 3--parametric family of hyperbolic 1--bridge genus one knots ((1,1)-knots, in short). In particular, we show that such knots admit two infinite series of lens space surgeries. Our work is related to a nice paper of Teragaito [16], since we represent his toroidal manifolds as 2--fold coverings of the 3-sphere branched over well--specified links
Dostoevskij mathematician (Part I)
No full textThe image of mathematics in Fyodor Dostoyevsky’s
novels is clearly negative. Notes from Underground
contain several famous and violent pages against
Mathematics, and this criticism is also echoed in other
masterpieces, such as Crime and Punishment and The
Possessed. Dostoevsky explicitly accuses mathematical
determinism of being arrogant and oppressive. On the other
hand, some of his main characters, such as Kirillov in The
Possessed and Ivan in The Brothers Karamazov, seem to
disclose unexpected mathematical sympathies. Here, in
Part I of a two-part article, we discuss Dostoyevsky’s
opinion of mathematics and, more generally, of science. In
Part II we also compare truth and freedom in mathematics
and in the vision of the Russian writer
Isometry Groups of Some Dunwoody Manifolds
No full textDunwoody manifolds are an interesting class of closed connected orientable 3--manifolds, which are defined by means of Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of lens spaces (possibly S^3) branched over (1,1)--knots. Here we study the Dunwoody manifolds which are cyclic coverings of the 3--sphere branched over two specified families of Montesinos knots. Then we determine the Dunwoody parameters for such knots and the isometry groups for the considered manifolds in the hyperbolic case. A list of volumes for some hyperbolic Dunwoody manifolds completes the paper
ON FOOTBALL MANIFOLDS OF E. MOLNAR
No full textA closed 3-manifold M is said to be hyperelliptic if it has an involution \tau such that the quotient space of M by the action of \tau is homeomorphic to the standard 3-sphere. We show that the hyperbolic football manifolds of Emil Molnár (1988) are hyperelliptic. Then we determine the isometry groups of suchmanifolds. Another consequence is that the unique hyperbolic dodecahedral and icosahedral 3-space forms with first homology group Z_35 (constructed by I. Prok in 1998, on the basis of a principal algorithm due to Emil Molnár, and byRichardson and Rubinstein in 1982) are also hyperelliptic
Fundamental Group and Covering Properties of Hyperbolic Surgery Manifolds
Get PDFWe study a family of closed connected orientable 3-manifolds obtained by Dehn surgeries with rational coefficients along the
oriented components of certain links. This family contains all the manifolds obtained by surgery along the (hyperbolic)
2-bridge knots. We find geometric presentations for the fundamental group of such manifolds and represent them as branched covering spaces. As a consequence, we prove that the surgery manifolds, arising from the hyperbolic 2-bridge knots, have Heegaard genus 2 and are 2-fold coverings of the 3-sphere branched over well-specified links
Topology of compact space forms from Platonic solids. I.
No full textThe problem of classifying, up to isometry, the orientable 3-manifolds that arise by identifying the faces of a Platonic solid was completely solved in a nice paper of Everitt [B. Everitt, 3-manifolds from Platonic solids, Topology Appl. 138 (2004) 253–263]. His work completes the classification begun by Best [L.A. Best, On torsion-free discrete subgroups of PSL_2(C) with compact orbit space, Canad. J. Math. 23 (1971) 451–460],Lorimer [P.J. Lorimer, Four dodecahedral spaces, Pacific J. Math. 156 (2) (1992) 329–335], Prok [I. Prok, Classification of dodecahedral space forms, Beiträge Algebra Geom. 39 (2)(1998) 497–515], and Richardson and Rubinstein [J. Richardson, J.H. Rubinstein, Hyperbolic manifolds from a regular polyhedron, Preprint]. In this paper we investigate the topology of closed orientable 3-manifolds from Platonic solids. Here we completely recognize those manifolds in the spherical and Euclidean cases, and state topological properties for many of them in the hyperbolic case. The proofs of the latter will appear in a forthcoming paper
CUSPED HYPERBOLIC 3-MANIFOLDS FROM SOME REGULAR POLYHEDRA
No full textWe illustrate some topological properties and give surgery descriptions of the cusped hyperbolic orientable 3–manifolds obtained by face pairings of the regular octahedron and the regular cube. Some applications and connections with the work of several authors (quoted in the references) complete the paper
Engineering students' use of scaffolding elements within digital tasks concerning planar integration domains
No full textIn this paper, we focus on a sequence of digital tasks involving the representation of subsets of the plane as normal domains. We investigate the role of scaffolding elements provided to supports Engineering students' activities with the tasks. The study focuses on 63 volunteer Engineering freshman. Using qualitative methods, we carried on the combined analysis of video recordings of the students' interaction with the tasks in small groups and their individual answers to a survey after the activity. The main result of the data analysis is the identification of three categories of students' behaviours concerning their use of the provided scaffolding elements. These categories reflect different ways of grasping the scaffolding, purposes and levels of awareness by the students
Fostering Engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks
No full textWe designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics
Platone e la matematica, parte I
No full textEsaminiamo e commentiamo la matematica presente nel pensiero e nell’opera di Platone, nella prospettiva di un laboratorio per docenti e studenti delle scuole superiori
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