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A generalized Desargues configuration and the pure braid group

Raul Cordovil, António Guedes de Oliveira, Michel Las Vergnas
1996 Discrete Mathematics  
This configuration, as a matroid, is a Desargues configuration if d = 5, and the union of (~) such configurations if d > 5.  ...  coloured) braid group on d strands.  ...  , including the Desargues configuration.  ... 
doi:10.1016/0012-365x(95)00152-m fatcat:li33gjt3rnaj3msebhh3twsng4

Fundamental Group of Desargues Configuration Spaces [article]

Barbu Berceanu, Saima Parveen
2011 arXiv   pre-print
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.  ...  The k th pure braid group of M is the fundamental group of F k (M ).  ...  The first group, isomorphic to Z 3 , is generated by the pure braids a, b, c, hence their images in π 1 (D I 0 ) are given by the d d d d d d d d d • • • • • • • • • • • • d 0 1 \ {I 0 } A 0 1 B 0 1 a  ... 
arXiv:1102.1790v1 fatcat:cxhdpkrieng5bkavyrfm5tpvby

Page 991 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
and the pure braid group.  ...  When d = 5, the matroid is a Desargues configuration. Thus, for general d, these matroids can be regarded as generalizations of the De- sargues configurations.  ... 

Author index to volume 160 (1996)

1996 Discrete Mathematics  
Vergnas, A generalized Desargues configuration and the pure braid group (1-3) 105-113 Culik 1I, K., An aperiodic set of 13 Wang tiles (Note) , P.C. and P.L.  ...  Zhu, Existence of three HMOLS of types h" and 2"31 (l 3) 49-65 Caro, Y., On the generalized Erd6s-Szekeres Conjecture --a new upper bound (Note) (1 3) 229-233 Catlin, P.A., The reduction of graph families  ... 
doi:10.1016/0012-365x(96)90028-x fatcat:u744kdd5fvhqzporqrttciio7a

Unexpected Stein fillings, rational surface singularities, and plane curve arrangements [article]

Olga Plamenevskaya, Laura Starkston
2021 arXiv   pre-print
Using planar open books and Lefschetz fibrations, we describe all Stein fillings of the links via certain arrangements of symplectic disks, related by a homotopy to the plane curve germ of the singularity  ...  On the other hand, we show that if for a singularity with reduced fundamental cycle, the self-intersection of each exceptional curve is at most -5 in the minimal resolution, then the link has a unique  ...  class group of the punctured plane, so the two braids are braid-isotopic.  ... 
arXiv:2006.06631v4 fatcat:4tl5xykbrzbszdbn3ohskaonsa

Symmetries and Geometries of Qubits, and Their Uses

A. R. P. Rau
2021 Symmetry  
In particular, the fifteen generators of the continuous SU(4) Lie group for two qubits can be placed in one-to-one correspondence with finite projective geometries, combinatorial Steiner designs, and finite  ...  The symmetry SU(2) and its geometric Bloch Sphere rendering have been successfully applied to the study of a single qubit (spin-1/2); however, the extension of such symmetries and geometries to multiple  ...  Marceaux for several discussions and for the preparation of several figures.  ... 
doi:10.3390/sym13091732 fatcat:cj2otl37xrf2vie7qgfsgdawha

A generalization of fiber-type arrangements and a new deformation method

Michel Jambu, Stefan Papadima
1998 Topology  
We prove that for hypersolvable arrangements the quadratic Orlik-Solomon algebra is always Koszul and also use it to obtain a generalization of the lower central series formula of [14] .  ...  We describe the structure of the fundamental groups of hypersolvable complements and prove that their associated graded Lie algebras are always determined by a minimal combinatorial information.  ...  The group M B L is the classical Artin pure braid group on n strands [29, p. 160] . Combinatorially one may dualize and view B L\ LB L , via the standard inclusion CL\LCL.  ... 
doi:10.1016/s0040-9383(97)00092-x fatcat:xaarlyl7c5d77lxxcgscrdx33q

Page 416 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
., 98k:81316 Cordovil, Raul (with Guedes de Oliveira, Antonio; Las Vergnas, Michel) A generalized Desargues configuration and the pure braid group.  ...  The reduced Gassner representation restricted to a normal free subgroup of the pure braid group. (English summary) 98):20046 Bachmuth, S. Braid groups are linear groups. 98h:20061 Bardakov, V.G.  ... 

Master index of volumes 151–160

1997 Discrete Mathematics  
., A.G. de Oliveira and M.L. Vergnas, A general- ized Desargues configuration and the pure braid group Culik II, K., An aperiodic set of 13 Wang tiles (Note) Curran, S.J. and J.A.  ...  Achuthan Caro, Y., On the generalized Erdos-Szekeres Conjecture -a new upper bound (Note) independence systems (Note) Chari, M.K., Reversible shellings and an inequality for h-vectors (Note)  ... 
doi:10.1016/s0012-365x(97)90002-9 fatcat:jhdpq4lxr5cz5ctggxfuouj6ti

Notes on noncommutative geometry [article]

Igor Nikolaev
2015 arXiv   pre-print
A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises is attached.  ...  The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory.  ...  Artin introduced the notion of a braid; the braid is a simpler object than the knot or link and, moreover, the braids can be composed with each other so that one gets a finitely generated group.  ... 
arXiv:1503.05411v1 fatcat:tvxqel7uzffjljgcfl5yhvsyqq

Moduli spaces of ten-line arrangements with double and triple points [article]

Meirav Amram, Moshe Cohen, Mina Teicher, Fei Ye
2013 arXiv   pre-print
This result is obtained by considering the moduli space of a given configuration table which describes the intersection lattice.  ...  Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair.  ...  The second author was partially supported by the Oswald Veblen Fund of the Institute of Advanced Study in Princeton.  ... 
arXiv:1306.6105v1 fatcat:fffkdktbgvg6bfc65gnslpryzu

Jordan structures in mathematics and physics [article]

Radu Iordanescu
2011 arXiv   pre-print
For a more detailed treatment of this topic see - especially - the recent book Iordanescu [364w], where sugestions for further developments are given through many open problems, comments and remarks pointed  ...  The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included.  ...  (pure) states, and the lines and hyperplanes with the propositions which are not atoms.  ... 
arXiv:1106.4415v1 fatcat:2c4jb7f3uzbnvkpa4h366h4t5q

Biased graphs IV: Geometrical realizations

Thomas Zaslavsky
2003 Journal of combinatorial theory. Series B (Print)  
A gain graph is a graph whose oriented edges are labelled invertibly from a group G; the gain group.  ...  the vector representation, while two, in projective space, strongly generalize the theorems of Menelaus and Ceva.  ...  For any gain group we also give a vector-like permutation representation of GðFÞ and a closely related but purely logical representation as a system of two-term equations (Section 3).  ... 
doi:10.1016/s0095-8956(03)00035-2 fatcat:pdtpjm532jfy5ea3lzfqpzqoyi

Information Processor

Jia-Rey Chang
one to a generative one.  ...  As compared to the era of tools, such as paper and pen, the computer, in today's context has been heavily utilized and relied upon as a powerful instrument.  ...  for purely aesthetics driven Form Generation.  ... 
doi:10.7480/abe.2018.1.3750 fatcat:3fgcnwtqkzbkrlluqtpinvgsku

Analysis of Mathematical Fiction with Geometric Themes

Jennifer Rebecca Shloming
The authors' pedagogical approaches to delivering the geometric themes are also discussed. Applications from this study involve a pedagogical component that can be used in a classroom setting.  ...  This thesis demonstrated that regardless of background, the authors could write a mathematical fiction novel or short story with a dominant geometric theme.  ...  Group 2 thus far is comprised of a biologist/psychologist, a physician, and an astronomer. The last member of this group is a computer scientist.  ... 
doi:10.7916/d86w9j54 fatcat:jwwn3rgpcjfmhfo45qcilfxcny
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