INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
Spaces of nonpositive curvature arising from a finite algebra
CRISTIAN CONDE; GABRIEL LAROTONDA
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ACADEMIC PRESS INC ELSEVIER SCIENCE
Lugar: Amsterdam, Holanda; Año: 2010 vol. 368 p. 636 - 636
In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite von Neumann algebra, and the metrics introduced arise from the trace of the algebra. In spite of the noncompleteness of these manifolds, their geometry can be studied from the view-point of metric geometry, and several techniques derived from the functional analysis are applied to gain insight on their geodesic structure.