Chapter 411

Chapter 414

"that's all I want to say. This is the derivation process. If you look at it more than once, you can understand it. I don't want to talk about it many times." Cheng Nuo stretched out and stood up from his seat. "Chali, I'll withdraw first. If this happens, I'll just send the question directly. You're still far away from the experimental building."

He raised his wrist and looked at the time and pointed to the door. "It's too late. If there's nothing else, I'll leave."

"That Wait When Cheng Nuo walks a few steps to the door, Milo, whose face is changeable, calls Cheng Nuo.

"Sorry! I shouldn't have questioned your strength Milo apologized to cheno.

Cheng Nuo waved his hand indifferently, "an LA, an LA, I'm used to it, and I don't mean to hate you!"

"Believe it or not, I didn't really take it to heart." Cheng Nuo turned around, waved his back to the crowd, "let's go!"

A day of leisure time, Cheng Nuo can not be so wanton waste.

…………

The next day.

With his bag on his back, Cheng Nuo came to a cafe on the campus of MIT. He ordered a cup of coffee and began his work today while drinking leisurely.

According to the schedule of the project, today is the first formal meeting of the group on geometric homology.

Although the level of the research group is very high, which is composed of a full professor, two associate professors and a graduate student, the main content of the discussion is nothing more than the overall framework of the research, as well as the specific division of research tasks.

Putting on the headphones, Chennault and three professors in Princeton started talking.

Cheng Nuo: Hello, Hello, can you hear me clearly

Miller: ha ha, Tom, your voice sounds very young

Cheng Nuo didn't answer and asked, "is the group leader there?"

Huckleberry: just a moment. The boss is on the phone. It will be ready soon

Dozens of seconds later

Tom, I'm sorry for waiting. Now that everyone is here, let's stop chatting and get down to business! "

Miller: OK

Hutch: OK

Cheng Nuo: "OK."

After a few seconds of silence, there was a slight cough, and then Professor Bourne's voice sounded, "as we all know, the proposition of Cheng Nuo theorem directly connects algebraic varieties and complex algebraic varieties in geometry. At the same time, the homology method which only exists in topological space can be applied to clusters and generalizations

"I have to say that the impact of the proposition of Cheng Nuo theorem on our geometric world is too great. There is the young man named Cheng Nuo. Even I admire him very much. I really want to ask him if I can

Cheng Nuo in the headphones to hear this wave of praise for Cheng Nuo, but also some blush.

I am now Is it that good?

Fortunately, Professor Bourne soon ended this meaningless praise and continued to say solemnly, "the purpose of our subject is to deduce the homology theorem which is used in algebraic varieties on the basis of Cheng Nuo theorem, and then pass the homology Theorem..."

Professor Bowen's way of speaking seems to be very similar to the Chinese style leadership. It is clear that he said something in a few words, which was added by Professor Bourne for nearly half an hour.

Fortunately, this is a voice conference, and Cheng Nuo is still distracted. As for Miller and hatch, who are now in front of Professor Bourne, I'm afraid it's hard.

"I'll start with that. Next, let's express our opinions and put together the overall framework of the subject first. " Professor Bourne finally ended his nagging.

The atmosphere fell silent again.

Professor Miller broke the embarrassment. "Tom, can you say something?"

"Ah, me?" Cheng Nuo was stunned for a moment. He thought it was miller who wanted to speak first? After a long time, I want him to say.

He thought in his mind, "I'll give you my opinion."

"As we all know, homology is a positive functor in the category of topological spaces, that is, it does not change the direction of the arrow. At the same time, a series of axioms including exitionlemma are satisfied. On a chain complex, we have reduced degree operations, such as the boundary operation: DN: cn → Cn-1. After two boundary operations, we get 0: DN-1 * DN: cn → Cn-2 = 0.

" Let X be a d-dimensional smooth projective family over FQ, and let É = x-fq. On projective family x, we can define FX, f ^ 2x, f ^ 3x The FQ ^ n point set X (FQ ^ n) on the projective family x is exactly the fixed point set of the endomorphism f ^ NX: X → χ! "

"How to calculate the number of fixed point sets on projective clusters?" Before Cheng Nuo finished, Professor Miller couldn't help asking.

Cheng Nuo smiles and says slowly, "Lefschetz fixed point theorem!"

Miller: "Lefschetz fixed point theorem?"Cheng Nuo stressed, "yes, it's Lefschetz fixed point theorem!"

Let X be a compact differential real manifold, F: X → X be a differential mapping, a fixed point of F is a point Xinx such that f (x) = X. for a fixed point X of X, differential DF_ {x} Is the tangent space t_ {x} A linear transformation of X. a fixed point x is said to be nondegenerate if 1-df (x) is invertible. This condition is that the fixed point has "multiplicity 1"! "

Cheng Nuo said this paragraph almost without thinking.

"That's right. I didn't really react for a moment just now." There came Miller's voice.

Professor Bourne went on to say, "my entry point is similar to Mr. Tom's. Using the basic properties of homology group in topology, we construct a smooth algebraic projective family and use the fixed point set to cut in

Then professor bernault explained his idea.

It's the same thing.

In addition to some specific details, some of the differences between the advantages and disadvantages, the general content is the same.

Professor Miller is a major in topology. Although his understanding of geometry is not as good as that of the other three, as a young mathematician with little fame in the field of topology, he naturally has a deep understanding of the homology group of topology.

But even he, after Cheng Nuo's explanation, did not put forward any flaw to this plan.

Professor hatch has no objection.

Bourne made the decision immediately. "In that case, follow me and Tom's. As for those different details, the calculation process will be simpler depending on whose scheme is adopted

The entry point is fixed, and the rest is simple.

Although some things can't put forward specific treatment measures before the actual calculation results, it is not necessary to build a framework containing only bones.

After a morning of three cups of coffee, the framework is finally set up and the tasks are assigned.

In the eyes of Miller and Bourne, Cheng Nuo was naturally regarded as a mathematician of the same rank as them. Therefore, there was no advantage in assigning tasks.

Looking at the items in his task list, Cheng Nuo moves his fingers.

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