Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups

Z. Lučić; E. Molnär

doi:10.1007/bf01188679

Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups

Archiv der Mathematik ◽

10.1007/bf01188679 ◽

1990 ◽

Vol 54 (5) ◽

pp. 511-520 ◽

Cited By ~ 9

Author(s):

Z. Lučić ◽

E. Molnär

Keyword(s):

Isometry Groups ◽

Finite Area ◽

Fundamental Domains ◽

Combinatorial Classification

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Multiplicity-Free Schubert Calculus

Canadian Mathematical Bulletin ◽

10.4153/cmb-2010-032-x ◽

2010 ◽

Vol 53 (1) ◽

pp. 171-186 ◽

Cited By ~ 5

Author(s):

Hugh Thomas ◽

Alexander Yong

Keyword(s):

Algebraic Geometry ◽

Schubert Calculus ◽

Chow Ring ◽

Free Products ◽

Linear Basis ◽

Combinatorial Classification ◽

Schubert Classes ◽

Multiplicity Free

AbstractMultiplicity-free algebraic geometry is the study of subvarieties Y ⊆ X with the “smallest invariants” as witnessed by a multiplicity-free Chow ring decomposition of [Y] ∈ A*(X) into a predetermined linear basis.This paper concerns the case of Richardson subvarieties of the Grassmannian in terms of the Schubert basis. We give a nonrecursive combinatorial classification of multiplicity-free Richardson varieties, i.e., we classify multiplicity-free products of Schubert classes. This answers a question of W. Fulton.

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Combinatorial classification of quantum lens spaces

Pacific Journal of Mathematics ◽

10.2140/pjm.2018.297.339 ◽

2018 ◽

Vol 297 (2) ◽

pp. 339-365

Author(s):

Peter Jensen ◽

Frederik Klausen ◽

Peter Rasmussen

Keyword(s):

Lens Spaces ◽

Combinatorial Classification

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Quadratic-monomial generated domains from mixed signed, directed graphs

International Journal of Algebra and Computation ◽

10.1142/s0218196719500024 ◽

2019 ◽

Vol 29 (02) ◽

pp. 279-308

Author(s):

Michael A. Burr ◽

Drew J. Lipman

Keyword(s):

Directed Graphs ◽

Complete Characterization ◽

Combinatorial Structure ◽

Signed Directed Graph ◽

Odd Cycle ◽

Combinatorial Classification ◽

Special Case ◽

Text Condition

Determining whether an arbitrary subring [Formula: see text] of [Formula: see text] is a normal or Cohen-Macaulay domain is, in general, a nontrivial problem, even in the special case of a monomial generated domain. We provide a complete characterization of the normality, normalizations, and Serre’s [Formula: see text] condition for quadratic-monomial generated domains. For a quadratic-monomial generated domain [Formula: see text], we develop a combinatorial structure that assigns, to each quadratic monomial of the ring, an edge in a mixed signed, directed graph [Formula: see text], i.e. a graph with signed edges and directed edges. We classify the normality and the normalizations of such rings in terms of a generalization of the combinatorial odd cycle condition on [Formula: see text]. We also generalize and simplify a combinatorial classification of Serre’s [Formula: see text] condition for such rings and construct non-Cohen–Macaulay rings.

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Classification of compact lorentzian 2-orbifolds with noncompact full isometry groups

Siberian Mathematical Journal ◽

10.1134/s0037446612060080 ◽

2012 ◽

Vol 53 (6) ◽

pp. 1037-1050 ◽

Cited By ~ 2

Author(s):

N. I. Zhukova ◽

E. A. Rogozhina

Keyword(s):

Isometry Groups

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Some Hyperbolic 3-Manifolds with Totally Geodesic Boundary

Algebra Colloquium ◽

10.1142/s100538671000043x ◽

2010 ◽

Vol 17 (03) ◽

pp. 457-468 ◽

Cited By ~ 1

Author(s):

Agnese Ilaria Telloni

Keyword(s):

Fundamental Groups ◽

Isometry Groups ◽

Geodesic Boundary ◽

Totally Geodesic ◽

Cyclic Coverings

We construct a family of compact hyperbolic 3-manifolds with totally geodesic boundary, depending on three integer parameters. Then we determine geometric presentations of the fundamental groups of these manifolds and prove that they are cyclic coverings of the 3-ball branched along a specified tangle with two components. Finally, we give a classification of these manifolds up to homeomorphism (resp., isometry), and determine their isometry groups.

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