"What is a Manifold?"

"This paper argues that objects that can look like Euclidean space or other relatively simple space up close. ”

"Manifolds can have any dimension. ”

Here the theory of topology is introduced, and the topology of the geometry is regarded as completely soft, because all the deformations will keep the topology unchanged, and the analytical cluster is regarded as a hard ......"

Liu Fei stopped writing, and he sat on the balcony of the dormitory of the Natural Law University.

The breeze blows, the magnificent sky of the Holy Land of Science flashes with the power of various rules, and the brilliance of the aura falls on the rows of buildings, giving the world a special kind of tranquil beauty.

The spectacle glasses shimmer with a strange light.

Liu Fei looked up at the sky, his fingertips moved slightly, and he casually tore off the smoke full of annihilating power.

If someone is around, you can see that Liu Fei's right eye has turned into mysterious mercury gray.

The gray eyes are constantly flashing, and they have the ability to see through everything.

The light of reason, the book of mathematics, the mystical nature of 'reality' are fully opened.

Liu Fei has found the direction of solving the problem of differential geometry.

Redefine manifolds!

In the holy land of science, all knowledge will appear in a visible way, and Liu Fei's paper began to beat with the crystal green aura formula symbol.

Very happy.

"The first step is to imagine the existence of a borderless manifold, such as the Möbius Belt. Its essence is a two-dimensional compact manifold that can be embedded in a three-dimensional or higher-dimensional manifold. What used to be inside is now merged with the outside, making it only one-sided. ”

"If you pull two Möbius strips into a circle, and turn the bands into a cross cap, you form an unoriented plane in four-dimensional space—the Klein bottle. ”

Rumble!

The Mathematical Reiki instantly bloomed strongly in the paper, and the Möbius Belt and the Klein Bottle are ancient geometric mathematical problems that existed before the revival of Reiki, and they both belong to the theory in topology.

The emergence of 'manifolds' successfully brings the two into the same system.

The aura flickered, first a twisted 'Möbius Belt' appeared in the air, followed by an even more magnificent Klein bottle that could not appear in three-dimensional space.

The Klein bottle is a surface that can only be truly represented in a four-dimensional space, and its geometric state in three-dimensional space seems to intersect with itself.

In fact, the bottleneck of the Klein bottle passes through the fourth dimensional space and is connected to the bottom circle of the bottle, and does not pass through the wall of the bottle.

This makes the Klein bottle look complex and mysterious.

The power beyond dimension is always more awe-inspiring.

Two special geometric manifolds, which are difficult to see in the real world, are getting bigger and bigger, and the sky is rumbling more violently.

The world of knowledge seemed to sense that something new was about to emerge, and the aura of mathematics was like the breath of a giant, and with each agitation the range of the aura became more and more intense.

……

Department of Defense of the University of Natural Law.

The Minister of Defense, who was in charge of security guards, was in a hurry, and as soon as he fell asleep, he received a call from his subordinates saying that the aura layout within the laws of nature had fluctuated violently and was even in danger of being out of balance.

"Did you find the location?"

"Found, in the Dome School District. ”

The Minister of Defense was slightly stunned, the Dome School District is the residence of scholars above the master level.

There are no defenses entering there all year round, so as not to disturb the train of thought of the bigwigs.

In fact, the Dome School District does not need any defenses.

Could it be that a certain big bull is about to be promoted or has studied cross-era scholarship again?

The defense chief still couldn't rest assured: "Who is the adult on duty today?"

"Ms. Mercer. ”

The defense chief unconsciously conjured up a beautiful figure with an extremely aggressive appearance, like a female leopard.

"Report the situation to Ms. Mercer. ”

……

"If the two special manifolds are topological categories, then the manifolds of the differential mechanism are another. ”

Liu Fei introduced the measurement system of angle, arc length and volume into the manifold, forming a new differential measurement system.

In this way, the basic concept of manifolds has been formed.

He looked up, and the huge mathematical aura brought not only external visions, but also lightning and thunder in the temple of knowledge.

Countless mysterious reliefs of the mathematical pillars appeared with green crystal stripes, and those stripes flickered at the same frequency as the breath of a giant with aura outside.

The relevant definitions of manifolds are directly inscribed on this ancient column.

As the original creator of the redefinition of the concept of 'manifold', from then on, all academic forces related to manifolds could be used directly by Liu Fei bypassing the Book of Reiki.

This is the primordial power!

One after another, majestic ones were drawn like palaces of knowledge, pouring down from the sky.

The soul was in it, and looking at the majestic aura in the sky actually produced a terrifying feeling like a prehistoric flood and annihilation.

The aura brilliance of the Mathematical Pillar was a full third stronger than before, far surpassing the remaining seven pillars, and one of the surrounding aura dragons was particularly huge.

The concrete manifestation of the power of the school of differential geometry opened by Liu Fei formally.

At this moment, Liu Fei has a deeper understanding of his palace of knowledge.

This huge energy alone may be comparable to the aura power of ordinary scholars, and he may be extremely slow in the promotion of scholars, but in terms of the total amount of aura, it is estimated that he can crush the world's scholars.

At this point, the first step in the era of differential geometry was completed.

Two special manifolds well-known in mathematics hung high in the sky, unusually huge.

Not only the Ministry of Defense, but the entire university district can see those two shapes.

The forums of major universities exploded in an instant.

The geometry school has always been a high producer of mathematical school war scholarship, and many scholars have tried to warn the Möbius Belt and the Klein Bottle because of their particularity.

It's a pity that because there is no solid theoretical foundation, the war effect between the two has been poor.

Now that two special geometric formations appear high in the sky, does it mean that there has been a new breakthrough in the basic theory of geometry?

The dormitory area of the University of Natural Law, because the distance is closer, it is also more real.

Cantor Tesla excitedly looked at the aura geometry of the starry sky, and couldn't help but whisper: "It must be the masterpiece of a supreme master, and a new theory will appear in the mathematical school!"

And at the moment.

"Such wonderful geometric forms, it looks like you've written something amazing. A hoarse, magnetic voice rang out.

Liu Fei was startled, and subconsciously waved his hand and threw out a Mobius composed of a green aura frame and flew towards the other party.

Once included in the attack, the opponent will be directly two-dimensional to the Möbius plane, and will not be able to leave unless the academic is cracked or broken by force.

The visitor was also surprised and let out a surprised sigh.

Immediately after, a huge mathematical aura flashed around the opponent's body, and the book of aura appeared, smashing the Mobius belt one after another to crack the formula.

Finally, the moment before the Möbius belt touched the other party, the aura was exhausted and disappeared.

Liu Fei finally saw the other party's figure clearly.

On the side of the balcony, a tall, charismatic red-haired lady floats in mid-air, smiling at the corners of her mouth.

"Nice attack, much stronger than the Brains at the War Gate. ”