User talk:David M. Austin

From Wikipedia, the free encyclopedia

David,

I'm rewriting some of the Floer homology introduction that you rewrote, including some which is a revert to a previous version. The issue is that there isn't a unique thing known as "Floer homology" but rather a collection of theories that apply in different situations, but count similar things and share analogous properties. (In particular, I don't think they're generally known to be homology theories in the sense usually meant of satisfying the eilenberg-steenrod axioms. They are homologies of a chain complex, and one gets certain kinds of functoriality from that, but the behavior of various versions of floer homology/symplectic field theory have some characteristic behavior not necessarily present in homology theories of topological spaces/spectra (eg surgery exact triangles) but they're not known to have crucial things like mayer-vietoris to reduce computations to those on simpler spaces; it's difficult (though relevant and important) to relate the (various kinds of) floer homologies on spaces related by topological cut-and-paste things.

However, I recognize how the previous wording ("some sort of pseudoholomorphic curve") can be mistaken for imprecision rather than expressing the complexity of the situation. I'd be indebted if you have any thoughts on how to resolve this and/or if you would look at the new version (which i'll write over the next day or two).

happy new year! David Farris (talk) 02:12, 1 January 2008 (UTC)

[edit] Review of "Wiki Math" session

Hi. Please see Wikipedia_talk:WikiProject_Mathematics#.28Incomplete.29_Summary_of_Joint_Math_Meeting_.22Wiki_Math.22_session and feel free to make comments. --C S (talk) 20:00, 9 January 2008 (UTC)