30,758 research outputs found
Dimension of the Torelli group for Out(F_n)
Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use
combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space
which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated
(n at least 3). In particular, this recovers the result of Krstic-McCool that
T_3 is not finitely presented. We also give a new proof of the fact, due to
Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
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