1,720,982 research outputs found
(1,1)-Nodi e gruppi ciclicamente presentati
No full textIn questa contributo si presenta un sunto della tesi di dottorato in cui si studiano le proprietà degli (1,1)-nodi ed in
particolare i loro legami con i gruppi ciclicamente presentati
A Markov theorem for plat closure of surface braids in Dunwoody and periodic Takahashi manifolds
No full textIn this article we deal with the problem of finding equivalence moves for links in
Dunwoody and periodic Takahashi manifolds. We represent these manifolds using
Heegaard splitting and we represent the embedded links as plat closure of elements
in the braid group of the corresponding Heegaard surfaces. More precisely, starting
from an open Heegaard diagram for such manifolds, we determine the plat slide
equivalence moves algorithmically and compute them explicitly in some cases
A Blended Teaching Sequence for Introducing Eigentheory in a Large University Class
Full text linkWe present the design and implementation of a teaching sequence on eigentheory that aims at encouraging at facilitating students’ active participation in a class attended by a high number of students. We describe how the use of the online noticing board Padlet facilitates the implementation of activities in small groups during lectures. These activities are designed based on the results of a pilot study aimed at assessing students’ understanding of eigentheory notions. We analyze various types of data collected during and after the implementation, showing a positive response from both the course teacher and the students to this teaching and learning methodology
On the axioms of singquandles
Full text linkIn this paper, we deal with the notion of singquandles introduced in [I. R. U. Churchill, M. Elhamdadi, M. Hajij and S. Nelson, Singular knots and involutive quandles, J. Knot Theory Ramifications 26(14) (2017) 1750099]. This is an algebraic structure that naturally axiomatizes Reidemeister moves for singular links, similarly to what happens for ordinary links and quandles. We present a new axiomatization that shows different algebraic aspects and simplifies applications. We also reformulate and simplify the axioms for affine singquandles (in particular in the idempotent case)
The complexity of orientable graph manifolds
Full text linkWe give an upper bound for the Matveev complexity of the whole class of closed connected orientable prime graph manifolds; this bound is sharp for all 14502 graph manifolds of the Recogniser catalogue (available at http://matlas.math.csu.ru/?page=search
Design, Making and the Digitisation Trap
Full text linkThe article aims to investigate the evolutionary dynamics and critical issues emerging around makerspace communities,
collaborative design and prototyping spaces whose practices have radically impacted the world of education,
enterprise and social innovation. Through an exploratory approach, experts from the
maker movement and design students have been involved to understand the health of the model underlying makerspaces.
The perspective of the research is to graft the debate on the forms of these practices into the dichotomy
between physical and digital, socialization practices of design and the ability of these bottom-up models to work
on complex solutions.
A list of recurring conditions occurring at the time of the creation of these communities has been elaborated.
The discussion then covers risks and limitations of the physical dimension of makerspaces in relation with digitization
of operations and relations at every level, calling for a necessary re-thinking of co-design practices
Corrigendum to “Extending homeomorphisms from punctured surfaces to handlebodies” [Topology Appl. 155 (6) (2008) 610–621]
No full textAbstractWe correct the statements of Theorems 9 and 10 of [A. Cattabriga, M. Mulazzani, Extending homeomorphisms from punctured surfaces to handlebodies, Topology Appl. 155 (2008) 610–621], by adding missing generators, and improve the statement of Theorem 10, by removing some redundant generators
Knot quandle decompositions
Full text linkWe show that the fundamental quandle defines a functor from the oriented tangle category to a suitably defined quandle category. Given a tangle decomposition of a link L, the fundamental quandle of L may be obtained from the fundamental quandles of tangles. We apply this result to derive a presentation of the fundamental quandle of periodic links, composite knots and satellite knots
Knot quandle decomposition along a torus
Full text linkWe study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of its companion and pattern knots. General presentations of the fundamental quandles of a link in a solid torus, a link in a lens space and a satellite knot are described. In the last part of this paper, an algebraic approach to the study of affine quandles is presented and some known results about the Alexander module and quandle colorings are obtained
Strongly-cyclic branched coverings of (1, 1)-knots and cyclic presentations of groups
No full textWe study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1, 1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1, 1)-knots, through the elements of the mapping class group. We prove that every n-fold strongly-cyclic branched covering of a (1, 1)-knot admits a cyclic presentation for the fundamental group, arising from a Heegaard splitting of genus n. Moreover, we give an algorithm to produce the cyclic presentation and illustrate it in the case of cyclic branched coverings of torus knots of type (k, hk ± 1)
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