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Research at MSRI was supported in part by the Russian Fond of Fundamental Investigations grant N 96-01-847, by INTAS project 94-921, and by NSF grant DMS-9022140. We describe the theoretical background for a computer program that recognizes all closed orientable three-manifolds up to complexity 8. The program can treat also nonclosed threemanifolds and… (More)
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the ‘cubic’ point of view. Finite type invariants of knots and homology 3-spheres fit perfectly into this conception. In particular, we get a natural… (More)
Let G be a graph (1-dimensional CW complex) in a compact 3manifold M . Following , we will apply to the pair (M,G) certain simplification moves as long as possible. What we get is a root of (M,G). Our main result is that for any pair (M,G) the root exists and is unique. Similar results hold for graphs with colored edges and for 3-orbifolds, which can be… (More)
295 arXiv version: fonts, pagination and layout may vary from GTM published version Roots in 3–manifold topology C HOG-ANGELONI S MATVEEV Let C be some class of objects equipped with a set of simplifying moves. When we apply these to a given object M ∈ C as long as possible, we get a root of M. Our main result is that under certain conditions the root of… (More)
We establish two-sided bounds for the complexity of two infinite series of closed orientable 3-dimensional hyperbolic manifolds, the Löbell manifolds and the Fibonacci manifolds.
Gauss diagram formulas are extensively used to study Vassiliev link invariants. Now we apply this approach to invariants of 3-manifolds, considering a manifold as a result ML of surgery on a framed link L in S . We study the lowest degree case – the celebrated Casson-Walker invariant λw of rational homology spheres. This paper is dedicated to a detailed… (More)
CONTENTS Let M and P be Seifert 3-manifolds. Is there a degree one map
SIDEROPHILE ELEMENTS: IMPLICATIONS FOR THE Se/Te SYSTEMATICS OF THE BULK SILICATE EARTH A. X. Seegers 1 , E. S. Steenstra 1 , R. Putter 1 , Y. H. Lin 1 , J. Berndt 2 , S. Matveev 3 , N. Rai 4 , S. Klemme 2 , W. van Westrenen 1 1 Faculty of Earth & Life Sciences, Vrije Universiteit Amsterdam, NL (email@example.com), 2 Department of Mineralogy, University… (More)
Given a set of simplifying moves on 3-manifolds, we apply them to a given 3-manifold M as long as possible. What we get is a root of M . For us, it makes sense to consider three types of moves: compressions along 2-spheres, proper discs and proper annuli having boundary circles in different components of ∂M . Our main result is that for the above moves the… (More)
We describe theoretical backgrounds for a computer program that recognizes all closed orientable 3-manifolds up to complexity 8. The program can treat also not necessarily closed 3-manifolds of bigger complexities, but here some unrecognizable (by the program) 3-manifolds may occur.