Hilbert's 3rd Problem and invariants of 3-manifolds
| dc.creator | Neumann, Walter D. | |
| dc.date | 1997-12-04 | |
| dc.date | 1998-10-27 | |
| dc.date.accessioned | 2026-07-07T05:23:22Z | |
| dc.date.available | 2026-07-07T05:23:22Z | |
| dc.description | This paper is an expansion of my lecture for David Epstein's birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This `logical progression' makes a good story but distorts history a bit: the ultimate aims of the characters in the story were often far from 3-manifold theory. We start in section 1 with an exposition of the current state of Hilbert's 3rd problem on scissors congruence for dimension 3. In section 2 we explain the relevance to 3-manifold theory and use this to motivate the Bloch group via a refined `orientation sensitive' version of scissors congruence. This is not the historical motivation for it, which was to study algebraic K-theory of C. Some analogies involved in this `orientation sensitive' scissors congruence are not perfect and motivate a further refinement in section 4. Section 5 ties together various threads and discusses some questions and conjectures. | |
| dc.description | 29 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper19.abs.html | |
| dc.identifier | https://arxiv.org/abs/math/9712226 | |
| dc.identifier | http://arxiv.org/abs/math/9712226 | |
| dc.identifier | Geom. Topol. Monogr. 1 (1998), 383-411 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76409 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M99, 19E99, 19F27 | |
| dc.title | Hilbert's 3rd Problem and invariants of 3-manifolds | |
| dc.type | text |