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					FORSCHUNGSINSTITUT FÜR MATHEMATIK ETH ZÜRICH

MINICOURSE

SCISSORS CONGRUENCES IN SPHERICAL AND HYPERBOLIC GEOMETRY Johan Dupont, Aarhus Universitet, Denmark

Wednesday 28th April 2004

15.45 Uhr – 16.45 Uhr 17.00 Uhr – 18.00 Uhr

Hermann Weyl HG G43 Hermann Weyl HG G43

Abstract Two polytopes are called scissors congruent if they can be cut into the same finite number of subpolytopes such that the pieces of the two polytopes are pairwise congruent by means of isometries of the geometry in question. This notion occurs in connection with an elementary definition of the concept of “area” in the Euclidean plane and has a long history. Thus Hilbert (1900) stated as the third problem on his famous list, the challenge of finding two Euclidean polyhedra of the same volume that are not scissors congruent. This problem was immediately solved in this form by M. Dehn (1900), who introduced additional necessary conditions for two polyhedra to be scissors congruent and showed that these are not satisfied for the regular cube and regular tetrahedron. In recent years scissors congruence has been studied from the point of view of group homology and algebraic K-theory. In the talks we describe some of the results from this development especially in connection with the study of the CheegerChern-Siimons invariant in 3-dimensional spherical and hyperbolic geometry.

Internet Æ http://www.fim.math.ethz.ch


				
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