Volume 14 (2008)

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Roots in 3–manifold topology

Cynthia Hog-Angeloni and Sergei Matveev

Geometry & Topology Monographs 14 (2008) 295–319

DOI: 10.2140/gtm.2008.14.295

arXiv: 0904.1531

Abstract

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 any object exists and is unique. We apply this result to different situations and get several new results and new proofs of known results. Among them there are a new proof of the Kneser–Milnor prime decomposition theorem for 3–manifolds and different versions of this theorem for cobordisms, knotted graphs, and orbifolds.

Keywords

3-manifold, connected sum, prime decomposition

Mathematical Subject Classification

Primary: 57N10

Secondary: 57M99

References
Publication

Received: 8 October 2006
Accepted: 19 March 2007
Published: 29 April 2008

Authors
Cynthia Hog-Angeloni
Fachbereich Mathematik der Universität Frankfurt
Postfach 111932
60054 Frankfurt
Germany
http://www.math.uni-frankfurt.de/~angeloni
Sergei Matveev
Chelyabinsk State University
129 Kashirin Brothers St.
454021 Chelyabinsk
Russia