Name
Title | ||
|---|---|---|
Algorithmic aspects of branched coverings II. Sphere bisets and their decompositions. |
Abstract | ||
|---|---|---|
consider the action of class groups, by pre- and post-composition, on branched coverings, and encode them algebraically as mapping class show how the class biset of maps preserving a multicurve decomposes into class bisets of smaller complexity, called class We phrase the decision problem of equivalence between branched self-coverings of the in terms of the conjugacy and centralizer problems in a class biset, and use our decomposition results on class bisets to reduce these decision problems to small class bisets. This is the main step in our proof of decidability of Thurston equivalence, since decidability of conjugacy and centralizer problems in the small class bisets are well understood in terms of linear algebra, group theory and complex analysis. Branched coverings themselves are also encoded into bisets, with actions of the fundamental groups. characterize those bisets that arise from branched coverings between topological spheres, and extend this correspondence to maps between spheres with multicurves, whose algebraic counterparts are sphere trees of A concrete outcome of our investigations is the construction of a Thurston map with infinitely generated centralizer --- while centralizers of homeomorphisms are always finitely generated. |
Year | Venue | Field |
|---|---|---|
2016 | arXiv: Group Theory | Topology,Linear algebra,Combinatorics,Algebraic number,Algebra,Group theory,Conjugacy class,Decidability,Torus,Centralizer and normalizer,Mathematics,Endomorphism |
DocType | Volume | Citations |
Journal | abs/1603.04059 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Bartholdi | 1 | 27 | 8.74 |
| dzmitry dudko | 2 | 0 | 0.68 |