What about works by Michael Friedman? And his protege, Vyacheslav Krushkal?
Mohamed, if you call yourself an engineer, what makes you believe that you are obliged to write answers? Your long reply is interesting , however, some references would be helpful.
Thank you Mohamed! What about this book ?
http://www.amazon.com/Wild-World-4-Manifolds-Alexandru-Scorpan/dp/0821837494/ref=sr_1_1?ie=UTF8&qid=1433945309&sr=8-1&keywords=scorpan&pebp=1433945311042&perid=29C9729C89F447D1B22A It is saying that 4 dimensional topology is very special. Fractals and all around them-these are just words. If I will call you not Mohamed but Arkady, you are going to stay Mohamed anyway. But if you believe in mathematics, it is quite ok to have smooth things in dimensions,say, 3 or 5 but it is dimension 4 which causes troubles.....So these fuzzy things is OK to implement in any dimension, e.g. the way Nottale is doing, but mathematics will support these ideas only if you are talking about 4 dimensional topology.
Here is the reference supporting what i just said
http://ac.els-cdn.com/S0166864115002382/1-s2.0-S0166864115002382-main.pdf?_tid=7cc50f3a-0f88-11e5-b4d4-00000aacb360&acdnat=1433951638_13750762461f99973c3dea579179f47c
Please, take a look at this
http://arxiv.org/abs/0906.1373 This is as close to fractals as i was able to find for you. However, fractals are not the goal in itself, just a tool. Incidentally , while working in polymer physics, i've learned about fractals a lot + ,of course, i knew the father of fractals Beniot in person and he also always remembered me by my 1st name.We had together many nice dinners and evenings.
A this moment I am finishing a paper which, I hope will be of interest to both physicists and mathematicians.I tend to stick to mathematicians when it comes to the way I handle things. Big names in physics do not impress me. Incidentally, even E. Witten is harshly criticized among many mathematicians....They really disregard his work for which he got the Fields Medal...
Yes, Golden mean paper is good.But at this moment I will not be able to incorporate it into what I have already.May be when I will post my paper to arxiv.org, submit it to Nuclear Physics B, then we can think about what else we can do with all this. Thank you anyway for this paper.It is indeed good!
Fine, here is the reference for you
http://repositories.lib.utexas.edu/handle/2152/24933
as sign of my gratitude
One considers a contractible 4-manifold, with boundary the 3-sphere. An example is the usual 4-ball. The question is: is this 4-manifold isomorphic to the 4-ball? In the TOP category the answer is yes by Michael Freedman. But in the PL or DIFF category the answer is not known today. If a counterexample would exist it would be called a fake 4-ball.
Many thanks, Claude! At the level you just described I am aware of these things and even more...However, my biggest concern is about the relationship between the slice/doubly slice knots/links and such type of 4-manifolds....
Dear Arkady, I am not an expert about the relation with doubly sliced knots. Sorry, Claude
Dear Claude, still many thanks. I can see that you are working in knot theory...I am not.However, my research had brought me into these topics.They are not just a casual curiosity for me.And, surely, I am not checking erudition of others.
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