Hilbert's Third Problem and Scissors Congruence Groups
Speaker:Kevin Hutchinson (UCD)Time: 4.00 PM
Date: Monday 15th April 2013
Location: Casl Seminar Room (Belfield Office Park)
Abstract:
Hilbert's third problem was to find two polyhedra of equal volume neither of which can be subdivided into finitely many pieces and re-assembled to equal the other (we say they are 'scissors-congruent' if this can be done). It was solved in 1900 by Max Dehn, who introduced a new invariant of (scissors-congruence classes of) polyhedra for the purpose. Much later, in 1965, J. P. Sydler showed that volume and
Dehn invariant are a complete set of invariants for classes of polyhedra in 3-dimensional Euclidean space. However, the corresponding problems for hyperbolic and spherical space have been much studied in the last thirty years because of their connections with K-theory, motivic cohomology, regulators and polylogarithms, homology of Lie groups and several other topics of current interest. I will give an overview of the history of these questions and discuss some recent developments.
Series: Algebra Seminar Series
Social Media Links