From the SelectedWorks of James T Struck
February 3, 2013
Poincare Conjecture Can be Proven, Disproven,
and Shown to Have No Relationship Between 3
Manifolds and 3 Spheres-How Science Magazine
Incorrectly Oversimplified the Poincare
Conjecture by Crediting Dr. Grigori Perelman of
Russia Alone with A Solution
James T Struck
Available at: http://works.bepress.com/james_struck/33/
Poincare Conjecture Can be Proven, Disproven, and Shown to Have No Relationship Between 3
Manifolds and 3 Spheres-How Science Magazine Incorrectly Oversimplified the Poincare
Conjecture by Crediting Dr. Grigori Perelman of Russia Alone with A Solution
From Wikipedia.org accessed 2/3/2013, “In December 2006, the journal Science honored the
proof of Poincaré conjecture as the Breakthrough of the Year and featured it on its cover.[5]
^ a b Mackenzie, Dana (2006-12-22). "The Poincaré Conjecture--Proved". Science (American
Association for the Advancement of Science) 314 (5807): 1848–1849.
doi:10.1126/science.314.5807.1848. PMID 17185565. ISSN: 0036-8075.
Science Magazine oversimplified the Poincare Conjecture when Perelman’s discussion was
described as breakthrough of the year. While a breakthrough possibly, my disproof and showing
of no relationship are just as important.
A conjecture can be proven, disproven, and no relationship shown or necessary. This third type
of conjecture response "No Relationship necessary" is a possible advance in mathematics that
conjectures can be responded to with proofs, disproofs and a finding of a lack of relationship.
The entire Poincare conjecture debate neglected to consider this third conjecture response that a
manifold does not have to be related to a 3 sphere. Henri Poincare was a human person who
lived in the 19th century with some problems like association with a cousin who was involved in
running France and some disabilities like some diphtheria history too.
Martin Luther King Junior said something like "Freedom is expensive." (Catholical Theological
Union poster 1/29/2013) Treated as a math conjecture "Freedom may or not may not expensive"
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one would be able to prove that sometimes freedom is costly and sometimes freedom is
inexpensive. One can consider cases where one is free and unfree.
1. Freedom spending much money would produce much cost.
2. Freedom not spending any money would not produce cost.
3. Freedom making money or printing money would have a cost decrease effect as more money
would be produced.
Depending on cases conjectures can be proven, disproven and left moot or inconclusive. Case
studies are important to math and economics. Poincare's conjecture can similarly be left
inconclusive. One does NOT have to map a homeomorphic simply connected manifold to any 3
sphere. Proven, disproven and inconclusive. One can leave the homeomorphic simply connected
manifold alone and not map the manifold to any 3 sphere; conjecture left moot, inconclusive, or
not necessary. One does NOT need to map a manifold to a 3 sphere. A manifold and 3 sphere
can exist without being mapped to each other. A manifold IS NOT necessarily homeomorphic to
a 3 sphere. One can have a manifold and a 3 sphere and not see them as mapping to eachother.
The Poincare Conjecture can be proven as in Perelman, disproven as in Struck below and said to
be inconclusive because I do not need to map a 3 manifold to a 3 sphere.
"Cow is jumping over moon" can be disproven, proven, shown inconclusive. Cow is jumping
over moon, not jumping, cannot tell if it can jump. Similarly Conjecture proven by Perelman,
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disproven by Struck manifolds change so mapping does not have to be one to one and shown
inconclusive we do not need to map a manifold to a 3 sphere.
James T. Struck BA, BS, AA, MLIS
2009-2010 Disproof by James T. Struck
Changing, Chaotic, Disappearing Number Systems Allow Disproving the Poincare
Conjecture-Perelman's Refusal to Accept the Field's and Clay Medal Opening Up More
Discussion of the Conjecture
James Timothy Struck
<http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1058483>
July 6, 2010
Abstract:
Changing, Chaotic, Disappearing Number Systems Allow for Disproof of the Poincare
Conjecture "The Poincaré conjecture says that a 3-dimensional manifold which is compact, has
no boundary and is simply connected must be homeomorphic to a 3-dimensional sphere."
I do not want Perelman to lose his Clay, Fields or other prize money; I would like him to care for
his mom in Russia, etc. I have an older mother who is denied rights by guardians here in Illinois;
I want Perelman to be able to support his mother and not lose some of his prize money. Still this
is some disproof of the Poincare conjecture using altering, changing, chaotic shapes which one
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moment would be bounded, compact, simply connected and the next moment not homeomorphic
to a 3 sphere due to alteration in shapes or related numbers. After there is alteration of a manifold
to another shape, the new shape does not homeomorphically map to a 3 sphere. Poincare's point
may have been that manifolds are open to change and alteration and therefore would not
homeomorphically map after all modulations to a 3 sphere.
Much of the Western world has psychologically limited our brains to number systems similar to
Arabic or Roman numbers or Arabic numerals. We should go outside the box when thinking
about numbers and numerals and begin to conceptualize other number systems. We know that
early Mesopotamian number systems involved pictograms, but we can go beyond pictograms
into imagining other number systems. Part of using numbers to develop mental acuity can be
inventing new number and numeral systems. I have developed or conceptualized several number
systems over the course of my life-Chaotic numbers or geometric manifolds that change value in
a disorganized fashion Changing numbers or shapes, manifolds that change over some identified
interval. Disappearing numbers or shapes that have a value then do not have a value (my mom
Jane Frances would talk about "it just disappeared," so she contributed to this type of shape or
number). Another number systems is modulating numbers or shapes that change their value back
and forth from one value to another. Subinfinite numbers or shapes that are infinite in value but
not beyond finite or numbers that are countable but still infinite. Another numbers systems are
pure infinite numbers or shapes that are uncountable in any way and express pure infinity, dying
numbers or shapes that expire after some period of time, Laughing numbers or shapes that can be
conceptualized to have an interaction with other phenomenon. Imagining number systems can be
a part of our lives like we imagine our parents, our mothers, fathers, sisters, friends, God, our
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work, our lives, our pasts and the Universe. Invent a number system and even if someone else
invented it already, some helpful librarian or math professor can tell you or research for you the
previous inventor of the number system. These number systems allow for a disproof or denial of
the Poincare conjecture. Using any of these number systems one can imagine a manifold which
is compact bound and simply connected which is not homeomorphic to a three dimensional
sphere. The Poincare conjecture is based on one type of number system, topological shape and
geometric concepts.
If we define numbers or geometric shapes as disappearing, changing, chaotic, and dying ( or
what Poincare could have meant by manifold), then even though an object may at sometime map
from manifold to a three dimensional sphere, at another point in time the map is not
homeomorphic as the numbers or shapes have changed or disappeared or altered irregularly.
Manifolds can do the same thing-disappear, change, modulate and change chaotically. A
changing manifold is not going to map 1-1 to a 3 sphere as a manifold will always change to a
structure which no longer maps to the 3 sphere as the manifold is changing and altering.
Each of the above number systems or geometric system provides a disproof of the manifold to 3
sphere homeomorphic Poincare conjecture. Both Perelman's proof and my disproof may be valid.
I also disproved the Poincare conjecture by showing that changing objects do not have to map
one to one to a 3 sphere as the changing object is always changing. Here is a second disproof. A
simply connected closed charted area would be one which can be compressed to a point or get
close to a point in space. Spheres and donuts are considered to not be homeomorphic, but areas
of spheres, donuts can be compressed to points or be simply connected close manifolds. As
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spheres and donuts are not homeomorphic, simply connected closed manifolds on spheres and
donuts do not have to map homeomorphically to other 3 dimensional spheres. Put simply, areas
on spheres and donuts can be compressed to points, but a sphere cannot be stretched and bent
into a donut. Therefore the areas compressable to points on spheres cannot be stretched and bent
into areas compressable to points on donuts! Poincare's conjecture is therefore shown false.
2 disproofs and one showing of no relationship show that a human being called Henri Poincare
was putting forth a conjecture which can be proven, disproven and shown to be unrelated.
Science Magazine, the Clay Foundation and others who felt obligated to credit Perelman with a
proof simplified issues. We prove, disprove and show no relationship in drug studies,
sociological studies, statistical studies all the time.
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