232 research outputs found
Constructing Goeritz matrix from Dehn coloring matrix
No full textAssociated to a knot diagram, Goeritz introduced an integral matrix, which is
now called a Goeritz matrix. It was shown by Traldi that the solution space of
the equations with Goeritz matrix (precisely, unreduced Goeritz matrix called
in his paper) as a coefficient matrix is isomorphic to the linear space
consisting of the Dehn colorings for a knot. In this paper, we give a
construction of a Goeritz matrix from a Dehn coloring matrix, from which Dehn
colorings are induced. Moreover, if the knot diagram is prime, we give a purely
algebraic construction of a Goeritz matrix from a Dehn coloring matrix.Comment: 10 pages, 6 figure
City University: Sculptural Space
No full textView as one enters the sculpture garden; Inside the ecological reserve of the Ciudad Universitaria campus stands the Sculptural Space. It is a big round natural solidified lava bed enclosed by a circular enclosure platform, which includes two levels, and surrounded by 64 white triangular prisms that seem to radiate from its center, a bit like a sunflower. The outer diameter of the platform measures 120 meters. There are other large metal and stone sculptures made by contemporary artists surrounding this installation area, hence its name. The sculptors who participated in the design and construction of Sculpture Space include Federico Silva, Manuel Felguérez, Helen Escobedo, Sebastian, Hersúa and Mathias Goeritz. Source: Wikipedia; http://en.wikipedia.org/wiki/Main_Page (accessed 7/8/2010
CONSTRUCTING GOERITZ MATRIX FROM DEHN COLORING MATRIX
No full textIn 1933, L.Goeritz introduced an integral matrix associated to a knot diagram, which is now called a Goeritz matrix, and proved that the ab-solute value of the determinant of the matrix gives an invariant of a knot. Recently, it was shown that the Goeritz matrix is closely related to the Dehn coloring of knots. In this paper, for a knot diagram, we give an algorithm to construct a Goeritz matrix from a Dehn coloring matrix, from which Dehn colorings are induced, with some geometric information of the diagram. More-over, if the knot diagram is prime, we give a purely algebraic construction of a Goeritz matrix from a Dehn coloring matrix
The Goeritz groups of -decompositions
No full textA -decomposition of a link in a closed orientable -manifold
is a decomposition of by a closed orientable surface of genus into
two handebodies each of which intersects the link in trivial arcs. The
Goeritz group of that decomposition is then defined to be the group of isotopy
classes of orientation-preserving homeomorphisms of the pair
preserving the decomposition. We compute the Goeritz groups of all
-decompositions.Comment: 16 pages, 13 figure
Link colorings and the Goeritz matrix
No full textWe discuss the connection between colorings of a link diagram and the Goeritz matrix.</jats:p
GENUS-TWO GOERITZ GROUPS OF LENS SPACES
No full textMinistry of Education, Science, and TechnologyGiven a genus-g Heegaard splitting of a 3-manifold, the Goeritz group is defined to be the group of isotopy classes of orientation-preserving homeomorphisms of the manifold that preserve the splitting. In this work, we show that the Goeritz groups of genus-2 Heegaard splittings for lens spaces L(p, 1) are finitely presented, and give explicit presentations of them.Basic Science Research Program through the National Research Foundation of Korea (NRF
LINK MUTATIONS AND GOERITZ MATRICES
No full textExtending theorems of J. E. Greene [Invent. Math. 192 (2013), 717-750] and A. S. Lipson [Enseign. Math. (2) 36 (1990), 93–114], we prove that the equivalence class of a classical link L under mutation is determined by Goeritz matrices associated to diagrams of L
LINK MUTATIONS AND GOERITZ MATRICES
No full textExtending theorems of J. E. Greene [Invent. Math. 192 (2013), 717-750] and A. S. Lipson [Enseign. Math. (2) 36 (1990), 93–114], we prove that the equivalence class of a classical link L under mutation is determined by Goeritz matrices associated to diagrams of L
Karl Goeritz with his children Frank Stefan and Irene Beatrix Portraits Family
No full textAll three died aboard the S.S. Simon Bolivar when it was struck by a sea mine along the coast of England near Harwich, on 18 November 1939.Karl Goeritz, 1900-1939; Frank Stefan Goeritz, 1932-1939; Irene Beatriz, 1938-193
The reality of fiction: the ECO by Mathias Goeritz
No full textAbstract
This article covers the full biography of a building, the Experimental Museum El Eco, designed by Germanborn and Mexican émigré artist and architect Mathias Goeritz. It provides an approach intersecting the biography of the author, the history of the building, and prominent individuals of the two cultural traditions, German and Mexican, who participated in the creation of a very special and unique building: El Eco. On the one hand, the ethics of Expressionism, the interest in non-European art, the cult of primitivism and the aesthetic system of the pair of concepts abstraction-empathy, all stemming from German culture. On the other, the pantheistic religiosity of landscape, zoomorphism and anthropomorphism, the interest in masks, and the aesthetics of monumental scale, stemming from pre-Cortesian Mexican culture. Taking the stance of intertwining Mathias Goeritz parcours with those of individuals and issues from his German past and his Mexican future – highlighting the figures of Wilhelm Worringer, Paul Westheim, Luis Barragán, Edmundo O'Gorman, and Ida Rodríguez Prampolini – this article proposes a return trip from fiction to reality, following in the footsteps of the author and comparing them with the pathway of the very building El Eco
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