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On volumes of arithmetic quotients of S O ( 1 , n )

Mikhail Belolipetsky (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We apply G. Prasad’s volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of S O ( 1 , n ) . As a result we prove that for any even dimension  n there exists a unique compact arithmetic hyperbolic n -orbifold of the smallest volume. We give a formula for the Euler-Poincaré characteristic of the orbifolds and present an explicit description of their fundamental groups as the stabilizers of certain lattices in quadratic spaces. We...

One configurational characterization of Ostrom nets

Jaromír Baštinec (1991)

Mathematica Bohemica

Bz the quadrileteral condition in a given net there is meant the following implication: If A 1 , A 2 , A 3 , A - 4 are arbitrary points, no three of them lie on the same line, with coll ( A i A j ) (collinearity) for any five from six couples { i , j } then there follows the collinearity coll ( A k A l ) for the remaining couple { k , l } . In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration...

Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles.

Christian Léger (1991)

Revista Matemática de la Universidad Complutense de Madrid

We call metamorphosis of a given category an autoequivalence functor up to within natural equivalence. We show that, given a group G, the group of metamorphoses of the category of G-sets (as well as the corresponding group for ?sufficiently big? subcategories) may be naturally identified to the group of outer automorphism of G. We get by this way a natural description of a group of known operations on tessellations of a surface: the identity operation, the Poincaré duality, and four others which...

Ordinary differential equations and their exponentials

Anders Kock, Gonzalo Reyes (2006)

Open Mathematics

In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.

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