Scholar’s Advanced Technological System

"Auntie!"

Zhongshan International's villa, sitting in his study, is holding a pen at the desk and writing something about the Lu Zhou, sneezing without warning. Fiction.

"Who is thinking about me..."

Sucking his nose and whispering to himself, Lu Zhou continued to look at the draft paper in front of him, and the ballpoint pen on his hand was gently lit on the table.

"It's a bit difficult."

[...when n is greater than 2, the two n-dimensional complexes completely intersect x^n(d), and x^n(d') differentiates the homeomorphism if and only if their euler number, total number of times, 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 for smooth manifolds.

This statement may be a bit sloppy, but in fact, in differential topology, this is a fairly popular research direction, mainly studying the invariant nature of differential manifolds under differential homeomorphic mapping.

However, there is some trouble. Although Lu Zhou has a lot of research on differential manifolds and topology, there are not many researches on differential topology.

It can even be said that this is a completely new field for him.

However, there is nothing wrong with this situation. After all, Professor Chen Yang studied the Hodge conjecture, and his research on the Riemann conjecture was originally two very different problems.

Just because the hyperelliptic curve analysis method can be improved and applied to the Cauchy-Riemann equation and the Riemann surface promotion surface, it led to his association with this problem...

"I am really embarrassed, I am a fat tiger... Do you want to leave it alone?"

After thinking for a while, Lu Zhou shook his head and eventually drove this disappointing thought out of the brain.

And if you don't talk about it, you will get the result first. Even if you don't install it, it is not his style to give up in the face of difficulties.

Even though differential topology is not his research direction, with his understanding of differential manifolds and topological theory, there is no big problem in quickly becoming familiar with the research points in this field.

What's more, the research on Riemann's conjecture is now in the bottleneck. Instead of dying on a path that is not going to work, try to look up and see if there are no other interesting clues.

If you can bridge the gap between topology and complex analysis problems, you can't say that his hyperelliptic curve analysis can make a wonderful effect on the research of the Riemann zeta function...

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

Xiao Ai: [Master, instant coffee does not need to add sugar? (°°〃)

"...oh, in short, help me make a cup of coffee."

[Good, good master! (··*)

The drone floated from the shelf and flew outside the study.

Aside from the distracting thoughts in the heart, Lu Zhou concentrated all his attention on this draft paper in front of him.

The thumb topped the button cover and he wrote the first line of text on the paper with a pen.

Let f1, ..., fr be a homogeneous polynomial of the complex coefficients of the variables z0, ..., zn+r. This set of polynomials defines a complex algebraic cluster x in the complex projective space p^(n+r)...]

[At this time, x is called a complex complete intersection. If the complex dimension of x is n, when x is a smooth manifold, it is called smooth complex complete intersection, then x is a 2n-dimensional smooth closed manifold... 】

The first step has been done.

Lu Zhou’s eyes shimmered with excitement.

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

"With a 2n-dimensional smooth closed manifold as the entry point, establish an association on the complex projective space..."

Once a breakthrough has been opened in thought, the inspiration that rushes out is like a flood, and the block can't stop.

A line-like calculation like a note flows down in his pen like a rushing river, and soon a whole piece of draft paper has been filled with dense numbers and figures.

Time passes by, and there are more and more manuscript papers piled up on the table.

Xiao Ai, who was kneeling on the shelf, just sneaked aside. Since Lu Zhou banned it from randomly opening the camera, it was only available to the camera on the drone.

Although it seems a bit distressing to look at the owner's hard work, but this kind of creative work, it really can't help.

The sky outside the window gradually darkened.

The boat in front of the table, in addition to reaching out to open the table lamp at the corner of the table, there is no other action besides calculation.

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

As the sky outside the window gradually dim, not only the original smooth stroke gradually slowed down, and the sweat beads gradually ooze out from the front of the Luzhou.

The situation does not seem to be as optimistic as he imagined.

The more in-depth study of this problem, the more he discovered that the maze behind the problem was so complicated.

"Ah, ah... it’s so hard!"

I don't know if I walked into the dead end on the first few times. Finally, I was unable to live in the boat. I was incarnate and violently swearing. I will count the half of the draft paper that I can’t count on, and I will fall into the paper basket next to it. in.

"Is not right! If the proposition is established, it will not be that I have thought about it for so long..."

The ballpoint pen in the hand turned faster and faster, and the brows locked in the brow were staring at the original question, and the lips opened and closed.

"But the strange thing is that it can't prove that the proposition is wrong... no matter how many sets of parameters are taken in, you can get the result that matches the proposition."

With a sigh of relief, Lu Zhou pinched the pen that turned fast, opened the computer at the corner of the table, logged into the literature database, and entered a few lines of keywords.

The rows of papers retrieved in the row soon appeared in front of him.

After selecting a few tags, sorted by the number of citations, Lu Zhou quickly picked out a few top papers.

"... such an interesting question cannot be studied without anyone."

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

The mouth was softly read, and at this time Lu Zhou’s eyes suddenly lit up, and a series of interesting titles were keenly captured from the database.

The author of the paper is Professor Krek, a well-known big cow in the field of partial differential equations and topology, and this paper is a paper he published in the Yearbook of Mathematics in 1999. A little high.

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

In the eyes, there was a fascination of interest. Lu Zhou quickly downloaded the paper and looked at it along the body of the paper.

After about ten minutes, when he saw the paper carefully, the eyes of interest in his eyes suddenly turned into excitement.

"that's it!"

"I said, such an interesting question must not have been studied before. At least someone must have studied a similar subject!"

"If you can convert the problem of manifold classification into the calculation of some matching group... Mom, this is the last piece of puzzle I lack!"

Excited to get up from the chair, walked to the Luzhou next to the waste paper basket, and quickly pulled out the draft paper that had been smashed by him.

"Fortunately, it's just a little wrinkled, not shredded!"

Self-talking, Lu Zhou took this draft paper and returned to the chair to sit down, flattening the draft paper in his hand on the table, and rekindled the raging fighting spirit in his eyes.

"Get started!"

After all, the sound of the brushstrokes sounded again in the study.

This time, it continued until dawn until it stopped...