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Advisement on 4-manifolds: please suggest

  1. Jan 17, 2008 #1

    WWGD

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    Hi, everyone:
    I apologize if this is out of place. Please let me know if so, and
    feel free to remove.
    I am trying to get into the world of 4-manifolds. I was wondering how to
    get someone to help me get started. I have taken classes in diff. geom.
    and hyperbolic geometry, and my analysis , topology, functional analysis
    are pretty good (all grad-PHD level). I understand the topic is vast and
    complex-- therefore the need for advisement. I am hoping towork more on
    the analytic side (i.e, diff. manifolds) , maybe "Functional-Analytic" than
    the purely topological one, tho I understand there will be heavy topological
    aspects nonetheless. Could someone please suggest how to get advisement?
    (my school is not exactly what you'd call the nurturing or supportive type,
    and my request for help there was largely ignored, tho I was told--at least so
    I understood-- that if I could do the work on my own, that I could go on
    and work in the area.).
    I understand the topic is complex and very open-ended, so that I do not
    expect short -term results. I am also still pretty motivated to put in 8+
    hours/day 7 days /week. (I finally found a good energy drink to help me with
    it:) )

    Thanks for your suggestions.
     
  2. jcsd
  3. Jan 17, 2008 #2

    WWGD

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    Sorry, I think I may not hav ebeen clear with the frase :help getting started.
    I hav ejust heard the area is very vast and open -ended and that getting results
    is difficult. I would just like some ideas on how to approach the topic, understanding
    that it is up to me tyo do the work.

    Thanks Again.
     
  4. Jan 18, 2008 #3

    mathwonk

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    most interesting and acessible 4 manifolds are algebraic complex surfaces, so one possibility is to begin the study of complex surfaces, e.g. in the books of beauville

    http://www.amazon.com/Complex-Algeb...al-Society/dp/0521498422/ref=pd_sim_b_title_2

    , or of barth, peters, and van de ven.

    http://www.amazon.com/Compact-Complex-Surfaces-Surveys-Mathematics/dp/0387121722

    or look up the works of simon donaldson, or those of john morgan and robert friedman.

    http://www.amazon.com/exec/obidos/ASIN/3540570586


    unfortunately all but the book of beauville are very pricey. that makes beauville's wonderful book a great bargain, but it only discusses complex surfaces and not the new theory of diff'ble 4 manifolds due to donaldson et al...

    look up the notion of gauge theory, and works by mrovka.
     
    Last edited: Jan 18, 2008
  5. Jan 19, 2008 #4

    WWGD

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    Thanks for the advice, mathwonk. I am getting started right away.
     
  6. Mar 19, 2008 #5

    WWGD

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    Follow-up

    Mathwonk:

    I was wondering if you know of any proffessor working in the area of
    smooth/smoothable 4-manifolds. No one in my school is working on it
    at the moment, but it is acceptable to have a prof. outside of the system
    be the advisor. Thanks for any suggestions, recommendations.
     
  7. Mar 20, 2008 #6

    mathwonk

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    where are you? what about robert friedman of columbia?
     
  8. Mar 21, 2008 #7

    WWGD

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    Thanks, Wonk:
    I am at CUNY . I will contact Robert Friedman. Ozsvath from Columbia said he was not
    working on the area , and J. Morgan did not reply.
     
  9. Mar 22, 2008 #8

    mathwonk

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    Alexandru Scorpan of Univ of Florida at Gainesville has a well reviewed book on the topic, and Gordana Matic of UGA, may be willing as well, but they are not in your geographic area.
     
  10. Mar 26, 2008 #9

    WWGD

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    4-mfld. Follow-up

    Thanks for helping a Yankee, there, Wonk. I will contact G.Matic ( and her relative
    Otto ) .
    I wrote to Scorpan, Casson, others, see if he could suggest someone, tho with
    no answer yet. Friedman is not working in the area anymore.
    Maybe it's the Easter thing and everyone is out or on break.
    Please let me know of anyone else in the country, even if not in the northeast,
    who may be working in the area, since they may be able to refer me to someone here.

    Thanks.
     
  11. Mar 27, 2008 #10

    mathwonk

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    and that is pronounced "mah - titch".
     
  12. Mar 27, 2008 #11

    WWGD

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    Sorry. I'll try to come up with another bad joke.
     
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