Chapter 930

"Achoo!"

Zhongshan International's villa, sitting in his study, is holding a pen in front of his desk and writing something on the land boat. He sneezed without warning.

"Who is thinking about me..."

He took a sniff and murmured to himself. Lu Zhou continued to look at the draft paper in front of him, and the ballpoint pen in his hand gently lit on the table.

"It's a little difficult."

【…… When n is greater than 2, two n-dimensional complex completely intersect x ^ n (d), x ^ n (d ') differential homeomorphisms, if and only if their Euler number, total number and Pontrjagin class are equal. ]Strictly speaking, this is not a complex analysis problem, nor a traditional partial differential equation problem, but a very interesting classification problem about smooth manifolds.

In fact, it is a hot research direction in differential topology. It mainly studies the invariant properties of Differential Manifolds under differential homeomorphism mapping.

However, there are some troubles. Although there are many researches on differential manifold and topology, there are not many researches on the branch of differential topology.

Even it can be said that this is a completely new field for him.

However, there is no doubt that this will happen. After all, Professor Chen Yang studies Hodge's conjecture, which is quite different from his Riemann conjecture.

It is only because the hyperelliptic curve analysis method can be improved and applied to study the Cauchy Riemann equation and the generalized surface of Riemann surface that his association to this problem is aroused

"I'm really embarrassed Do you want to leave it alone? "

After thinking for a while, Lu Zhou shook his head, and finally drove the idea out of his mind.

Let's not say who is better than one to get the result first. Even if he doesn't pretend to be forced, it's not his style to give up in the face of difficulties.

Even though differential topology is not his research direction, but with his understanding of Differential Manifolds and topology theory, there is no big problem to be familiar with the research points in this field quickly.

What's more, the research of Riemann's conjecture has also fallen into a bottleneck. Instead of being stuck in a impassable Road, it's better to try to look around and see if there are any other noticeable clues.

If we can build a bridge between topology problems and complex analysis problems, we can't say that his hyperelliptic curve analysis method can play a wonderful role in the study of Riemannian zeta function

"Little AI, make me a cup of coffee, no sugar!"

AI: Master, instant coffee doesn't need sugar? (°ー°〃)]

“…… Long winded, help me make a cup of coffee. "

Good master! (?? *)]

the UAV floated up from the bookshelf and flew to the outside of the study.

Putting aside the thoughts in his mind, Lu Zhou focused all his attention on the draft paper in front of him.

With his thumb on top of the clasped pen cover, he wrote the first line on the paper with his pen.

Let F1 , FR is about the variable Z0 , Zn + R. This group of polynomials defines a complex algebraic family X in the complex projective space CP ^ (n + R) ]

[at this time, X is called a complex complete intersection. If x's complex dimension is n, when x is a smooth manifold, it is called a smooth complex complete intersection. At this time, X is a 2n dimensional smooth closed manifold ]The first step has been completed.

The eyes of the boat gleamed with excitement.

Although this feeling is very weak, he has a very obvious premonition that he has found the right way to the end of the maze.

In this paper, we take the smooth closed manifold of 2n dimension as the starting point, and establish the relation on the complex projective space

Once a breakthrough has been opened in thinking, the surging inspiration will flood out like a flood, which can not be stopped.

A line of calculations like notes poured down his pen like a running river, and soon the whole manuscript was filled with dense operators and numbers.

As time went by, more and more manuscripts were piled on the desk.

Lying on the bookshelf, AI steals by. Since the land boat forbids it to turn on the camera casually, only the UAV can use the camera freely.

Although it's a bit painful to see the owner's hard work, this kind of creative work can't help.

The sky outside the window gradually darkened.

In addition to reaching out to turn on the lamp at the corner of the next table, the land boat that lies at the table has no other action except calculation.

However, the situation does not seem to be moving in a more optimistic direction.

As the sky outside the window gradually darkened, not only did the original smooth strokes slow down, but also sweat began to seep from the forehead of the boat.It didn't seem as optimistic as he thought.

The more deeply he studied the problem, the more complex the maze hidden behind it was.

"Ah ah It's so hard! "

I don't know how many times I walked into the dead end, and finally I became a grumpy brother in an instant. I crumpled half of the draft paper that could not be counted, and threw it into the basket beside me.

"No! If the proposition is true, I can't think of it for so long... "

The ballpoint pen in his hand turned faster and faster. The boat with its eyebrows locked was staring at the initial problem, and his lips were opening and closing slightly.

"But it's strange that the proposition can't be proved wrong No matter how many groups of parameters are taken in, the result is consistent with the proposition. "

With a long breath, Lu Zhou grabbed the pen and turned it fast, opened the computer at the corner of the desk, logged in to the literature database, and entered several lines of keywords.

The papers, which were retrieved in rows, soon appeared in front of him.

After selecting several tags and ranking them according to the number of citations, Lu Zhou quickly picked out several top papers.

“…… It's impossible that such an interesting question has not been studied. "

"At least we should be able to find something similar."

He read it gently in his mouth, and then suddenly the eyes of Lu Zhou brightened, and a row of interesting titles were acutely captured from the vast database.

The author of this paper is Professor Kreck, who is famous in the field of partial differential equations and topology. This paper was published in the mathematical Yearbook in 1999, and it has been cited a little more frequently.

According to the description of its abstract part, the main content of this paper is to improve the theory of surgery, and transform the problem of manifold classification into the problem of some edge groups.

Gradually, a trace of interest appeared in his eyes. Soon, Lu Zhou downloaded the paper and looked at it line by line along the main body of the paper.

After about ten minutes, when he saw the paper carefully, the interested look in his eyes suddenly turned into an excited look.

"That's it!"

"I'll just say that such an interesting question can't have been studied completely before At least someone has studied a similar subject! "

"If we can translate the problem of manifold classification into the calculation of some collocation groups Mom, this is the last piece of puzzle I lack! "

Excitedly, he got up from his chair, walked to the boat beside the wastebasket, and quickly turned out the manuscript paper he had crumpled into a ball.

"Fortunately, it's just crumpled, not torn off!"

Talking to himself, Lu Zhou took the draft paper and went back to the chair again. He spread the draft paper in his hand on the table, and his eyes lit up again.

"It's about to start!"

After that, the brush strokes in the study sounded again.

This time, it didn't stop until dawn