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jeanluct / ttauto

C++ library for building train track automata for homeomorphisms of punctured discs
GNU General Public License v3.0
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find the train track map #3

Open jeanluct opened 9 years ago

jeanluct commented 9 years ago

Given that we find the transition matrix, is is hard to find the actual train-track map?

jeanluct commented 9 years ago

See this folder for some notes.

jeanluct commented 9 years ago

We should be able to this by accumulating the map piece-by-piece in traintrack::fold. We need a way to label main and infinitesimal edges consistently (with orientation). That's probably already done in some way using the coding.

jeanluct commented 9 years ago

The positive edge orientation can be taken as that traversed by the coding?

jeanluct commented 9 years ago

Can use multigon_index and multigon_prong_index to label the infinitesimal edges around multigon.

Main idea: make a "free word" class (basically an ordered list). Derive from it main edges (numbered by some edge_index) and infinitesimal edges (numbered using a combination of multigon_index and multigon_prong_index.). The latter would also contain a way to print a string describing what they are, or a more cryptic number for storage.

Main problem is inverses... But ignore those for now.

jeanluct commented 9 years ago

See branch iss003-tt-map. I think I need to define "small" train track maps for each step (mappings of each generator to a word), which could then be applied successively, as in the notes.

jeanluct commented 9 years ago

Ok, getting closer in 3fe0a02! I can get the basic map from the matrices. Not 100% sure it's right, though. In particular I'm not sure I'm doing the right thing as far as orientation is concerned. Need to draw some examples.

I think I need to rewrite so that it uses recursion directly instead of guessing the tt map from the matrices. Then I can likely pick up the infinitesimal edges as I go.

TODO: Maybe write the ttmap equivalent of mathmatrix_permplus1.