Talk:Monodromy

Untitled[edit]

"S" means "solution space" for the diffeqs? May want to explain this. - Gauge 21:31, 1 Aug 2004 (UTC)

Formal?[edit]

The formal definition in the article is really a precise definition of monodromy in one particular (algebraic) context. I think this is misleading, and that this section should do one of the following:

Give a sufficiently general definition to encompass the most common use of the term
Provide several definitions that cover the most common ways in which the term is used
Have its title changed to indicate it only defines monodromy of a Galois field extension

--David Dumas 19:03, 18 July 2005 (UTC)[reply]

Yes, it certainly needs work. I'll change the section title to mention Galois theory, for the moment. Charles Matthews 19:11, 18 July 2005 (UTC)[reply]

I've added the technical definition using covering spaces, and I've left the perhaps redundant intuition at the end of the article, hoping a more seasoned wikipedian will know what to do with it. --Orthografer 19:17, 18 February 2006 (UTC)[reply]

Reiner: Sept 10, 2010: Whatever you are going to change: please leave the straightforward explanation of the origin of the word monodromy in there - it provides perhaps not just for me a moment of clarity. It is usually extremely difficult to learn anything of depth in mathematics by reading wiki's: Even though I have a degree in physics I find myself endlessly clicking from one "formal definition" to the next when trying to figure out something specific, about which I may have only half knowledge. Most writers in math wiki's seem to really know their stuff, and often the connections between different topics somehow shine through, but nevertheless the final product present themselves to the reader like a complete jungle of hyper-links. Power to the generalists who understand to combine the precise definitions and proofs with a still accurate "in-a-nutshell" explanation and with references to the history of mathematical concepts. I wish there was some kind of hierarchy, road map, or tree like presentation of these vast fields. —Preceding unsigned comment added by 97.80.103.33 (talk) 14:48, 10 September 2010 (UTC)[reply]

Merge from monodromy operator[edit]

The article monodromy matrix is currently a two-line statement about ODE's that is completely incoherent. I think its talking about the the very one and the same monodromy as here, taken from the perspective of an ODE textbook. There's something about a fundamental matrix, but it seems to be more of an adjoint representation of the monodromy group by ODE's or something like that I can't tell. linas (talk) 18:35, 2 September 2012 (UTC)[reply]

I think this refers more to Floquet theory Felix1012 (talk) 15:17, 5 July 2013 (UTC)[reply]

On the figure purporting to depict the example log(z)[edit]

Concerning the figure (File:Imaginary_log_analytic_continuation.png) associated with the Example, I find it very confusing. I am quite familiar with Riemann's construction associated with connecting a series of sheets by cutting along an axis. As mentioned in this section, the correct depiction is that of the Helicoid.

The circles on the surface shown are even more confusing. The circle described in the Example is |z|=0.5, which gets lifted to a helix in Riemann's construction. That helix would have Re(z) and Im(z) oscillating between [-1/2,1/2], with Im(log(z)) progressing by 2\pi per cycle.

I suggest removing this figure or replacing it with an appropriately modified version of the Helicoid figure (File:Helicoid.svg).

MidwestGeek (talk) 04:51, 3 October 2017 (UTC)[reply]

Monodromy and Perverse Sheaves[edit]

This page should discuss monodromy results found in perverse sheaves. In particular, simple examples of monodromy should be cited and shown how/where to find proofs.

This should reflect current usage, not the original/historical meaning[edit]

This article (June 12/2021) starts out discussing the original historical meaning of the word monodromy, whereas the common usage is different to the original meaning. If you google "nontrivial monodromy" this will be clear: when people say "nontrivial monodromy" they mean that it is not single valued. Thus the current usage of the word monodromy, is what was historically called polydromy. This is discussed in section 1.2 of arXiv:1507.00711: where the author suggests the sensible attitude: "We shall also adhere here to the prevailing attitude, to call monodromy what should really be called polydromy, and we explain it now". — Preceding unsigned comment added by Ccgim (talk • contribs) 07:58, 12 June 2021 (UTC)[reply]