周秉根教授破解五个世界著名数学猜想想的英文稿

The two papers(Chines language) of the abstract published on the

Capital magazine(China ),No.5,2012

T estify on the Poincare Conjecture

Zhou B inggen

（College of T erritoral Resources and T ourism，Anhui Normal University，Wuhu，Anhu，241002，China）

Abstract（The abstract is more correct than my Chinese papers on this problem）The Poincare conjecture is a important theory problem of the topology. The topology is studying the characteristics of the not change of the egometrical figure under topology change. The lenth, area and the collinear feature can be changed by the topology change but the number of the“dimension”,connectedness and“hole”and so on may not be changed. The Latter is just the topology characteristics. The two figures with the change each other by the topology change is called the homeomorphism.

2006, the Poincare conjecture is confirmed the testimonial by the mathematician of the Russian named Grigory Perelman. But, Grigory Perelman didn’t accept the John Charles Fields A ward. The author of this paper thinkes that Grigory Perelman maybe have the misgivings for the correct feature of his testimonial, so he didn’t accept the award.

When I(the author of this paper) study the theory of relativity, I found that the locus of the body motion:it is one point when body is motionless,it is one line along the one dimension space motion, it is one scope along the two dimensions space motion,it is one bulk along the three dimensions space motion, it is one sphere (plane is one circular) along the four dimensions space motion, it is one ellipsoid (plane is one ellipse )along the five dimensions space motion, it is one flat ellipsoid ( plane is one flat ellipse)along the six dimensions space motion,……the more the dimension, the more flat ellipsoid( plane is more flat ellipse ), ……turn back to one line and one point,and it reappear circulation.

The change law of the geometrical figure is as follows,according to the topology characteristics and the locus of the boby motion along many dimension space:

①It is one point when body is motionless,point enlarge is one sphere, the point

and point is alone connectedness,have homotopy extension property,so the point and point is the homeomorphism;

②It is one line along the one dimension space motim,straight line, curve and

circumference curve is all alone connectedness, have homotopy extension property, so the line and line is the homeomorphism;

③It is one scope along the two dimensions space motion,the plane,surface and

the area of circle etc.is all alone connectdness, have homotopy extension property, so the scope and scope is the honmeomorphism,two dimensions space hasn’t spherical surface;so the scope and scope is the homeomorphism ;

④It is one bulk along the three dimensions space motion, the cuboid, cube,

polyhedron and so on can be change each other, they are all alone connectedness, have homotopy extension property, so the bulk and bulk is the homeomorphism. But, here we must pay attention to the bulk and the spherical surface don’t be the homeomorphism. Because three dimensions space has only the locus of the bulk and hasn't the spherical surface. The spherical surface is the locus of the four dimemsions space motion.

⑤It is one sphere ( plane is one circular ) along the four dimensions space

motion. When one bulk turn around another axle ,the locus is one sphere ( plane is one circuar ).And sphere has only the spherical surface, the scope and the bulk have not the spherical surface. The spheres are all alone connectedness, have homotopy extension property,so the sphere and sphere is the homeomorphism.

⑥It is one ellipsoid ( plane is one ellipse )along the five dimensions space

motion. When one sphere turn around another axle, the locus is one ellipsoid ( plane is one ellipse ). The sphere and the ellipsoid ( plane circular and ellipse )

are all alone connectedness, have homotopy extension property, so the sphere and ellipsoid, ellipsoid and ellipsoid is the homeomorphism.

⑦It is one flat ellipsoid ( plane is one flat ellipse ) along the six dimensions space

motion. The flat ellipsoid and the flat ellipsoid is alone connectedness, have homotopy extension property, so the flat ellipsoid and the flat ellipsoid is the homeomorphism.

⑧……the more the dimension, the more flat ellipsoid ( plane is more flat

ellipse ), ……so the flat flat ellipsoid and the flat flat ellipsoid is alone connectedness, have homotopy extension property,is also the homeomorphism.

⑨When the locus of the body motion turn back to one line and one point, the line

and line, the point and the point is alone connectedness, have homotopy extension property, is also the homeomorphism, ……and it reappear circulation.

⑩So ,the conclusion is: when the dimension is definited, the geometrical figure of the different form with the itself dimension is alone connectedness, have homotopy extendion property and is the homeomorphism.Along with the increase of the dimension, the point, line, scope, bulk, sphere, ellipsoid, flat ellipsoid, ……flat flat ellipsoid, ……line,point, ……have connectedness,have homotopy extension property and is the homeomorphism.

It shows the locus of the fluid motion can be changed in perfect order by the increase of the motion dimension. The fluid can be flow only in four dimension space. The fluid can't motion not have fall differ. And the locus of the celestial body motion is the ellipse, that it shows the celestial body motion have got the force influence with more than five dimensions space. So, the Poincare conjecture has important significane of the theory and practice.