Discrete Geometry and Topology

Discrete Geometry and Topology

by S. P. Novikov
     
 

ISBN-10: 082183147X

ISBN-13: 9780821831472

Pub. Date: 02/10/1993

Publisher: American Mathematical Society

This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that

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Overview

This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.

Product Details

ISBN-13:
9780821831472
Publisher:
American Mathematical Society
Publication date:
02/10/1993
Series:
Proceedings of the Steklov Institute of Mathematics Series, #196
Pages:
193

Table of Contents

Boris Nikolaevich Delone (on his life and creative work)1
On variations of positive quadratic forms (with applications to the study of perfect forms)11
Partitioning of Euclidean space into L-polytopes of some perfect lattices29
Spanier-Whitehead duality and the stability of the intersection of compacta53
Combinatorial questions of the two-dimensional Ising model57
Quadrillages and parametrizations of lattice cycles73
On mappings of cubic manifolds into the standard lattice of Euclidean space95
On the curvatures of tangent spheres99
On a nonregular partitioning of n-dimensional Lobachevsky space by congruent polytopes103
On a geodesic on a Seifert-Weber manifold107
Projective Euclidean geometry and noncommutative probability theory117
Three-dimensional spherical forms129
On the dissociation of point systems163
Homology on presheaves of sets173
Dual systems of integer vectors and their application to the theory of (0,1)-matrices179

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