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44

votes

6 answers

Does $\mathbb C\mathbb P^\infty$ have a group structure?

Does

$\mathbb C\mathbb P^\infty$ have a (commutative) group structure? More specifically, is it homeomorphic to

$FS^2$ , (the connected component of) the free commutative group on

$S^2$ ?

$\mathbb C\mathbb P^\infty$ is well known to have the homotopy…

asked Mar 31 '16 at 02:20

Ben Wieland

8,667

44

votes

1 answer

Useful, non-trivial general theorems about morphisms of schemes

I apologize in advance as this is not a research level question but rather one which could benefit from expert attention but is potentially useful mainly to novice mathematicians. I'm trying to compile a list of non-obvious theorems about morphisms…

asked Mar 24 '16 at 23:56

Saal Hardali

7,549

44

votes

4 answers

Applications of algebraic geometry to machine learning

I am interested in applications of algebraic geometry to machine learning. I have found some papers and books, mainly by Bernd Sturmfels on algebraic statistics and machine learning. However, all this seems to be only applicable to rather low…

asked Mar 19 '16 at 16:10

Lisp Rambo

443
1
5
5

44

votes

5 answers

Several Topos theory questions

Hey. I have a few off the wall questions about topos theory and algebraic geometry. Do the following few sentences make sense? Every scheme X is pinned down by its Hom functor Hom(-,X) by the yoneda lemma, but since schemes are locally affine…

asked Oct 24 '09 at 16:49

Steven Gubkin

11,945

44

votes

19 answers

introductory book on spectral sequences

I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand. Are there books or web resources that serve as good first introductions to spectral sequences? Thank…

asked Apr 22 '10 at 14:13

user2529

44

votes

2 answers

What algebraic group does Tannaka-Krein reconstruct when fed the category of modules of a non-algebraic Lie algebra?

Let

$\mathfrak g$ be a finite-dimensional Lie algebra over

$\mathbb C$ , and let

$\mathfrak g \text{-rep}$ be its category of finite-dimensional modules. Then

$\mathfrak g\text{-rep}$ comes equipped with a faithful exact functor "forget" to the…

asked Apr 15 '10 at 04:06

Theo Johnson-Freyd

52,873

44

votes

3 answers

When is a Homology Class Represented by a Submanifold?

Possible Duplicate: Cohomology and fundamental classes Given an oriented manifold

$M$ and an oriented submanifold

$\phi:N\to M$ we can obtain a homology class

$\phi_*[N]\in H_*(M)$ where

$[N]$ is the fundamental class of

$N$ . …

asked Apr 13 '10 at 01:15

Steve

2,223

44

votes

1 answer

Homotopy Type Theory: What is it?

My question is, broadly, what is the main project of Homotopy Type Theory (HoTT). I asked a professor who is likely to be correct and he say the following: There are three directions: Topologists are seeing type theory as a concise and convenient…

asked Mar 18 '15 at 00:49

James

541

44

votes

9 answers

How to start game theory?

I recently got interested in game theory but I don't know where should I start. Can anyone recommend any references and textbooks? And what are the prerequisites of game theory?

asked Mar 19 '10 at 20:42

Axiom

520

44

votes

1 answer

A topologist is not a mathematician - a small question

Years ago I read about a topologist who was to enter the states as an immigrant and was asked a question about his profession. He indicated he was a topologist, but as this was not included on the officer's list, he wanted to check him in as a…

asked Aug 08 '14 at 13:18

MathMan

545

44

votes

3 answers

Why aren't fields called "bodies" instead?

The discrepancy regarding the names of commutative division algebras in German and English has always startled me. In English they are called fields, whereas their original German name is Körper (hence the

$K$ ), a word which usually means "body" in…

asked Jan 22 '14 at 22:20

Dominik

3,007

44

votes

2 answers

What is known about the sum x^{n^2}/n?

It follows from a general theorem of Honda that the formal group with the logarithm

$x+x^{2^s}/2+x^{3^s}/3+x^{4^s}/4+\cdots$ has integer coefficients. I became interested in it because its

$p$ -typizations give the formal groups of the

$s$ th…

asked Oct 28 '13 at 11:48

მამუკა ჯიბლაძე

17,468

44

votes

4 answers

Truth of the Poisson summation formula

The Poisson summation says, roughly, that summing a smooth

$L^1$ -function of a real variable at integral points is the same as summing its Fourier transform at integral points(after suitable normalization). Here is the wikipedia link. For many years…

asked Feb 07 '10 at 23:19

Feb7

481

44

votes

2 answers

Applications of Lawvere's fixed point theorem

Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism

$A \to X^A$ which is point-surjective (meaning that

$\hom(1,A) \to \hom(1,X^A)$ is surjective), then every endomorphism of

$X$ has a fixed point…

asked Aug 17 '13 at 09:37

Martin Brandenburg

61,443

44

votes

9 answers

Homotopy as a general organizing principle

One of the realizations that led to the development of Homotopy Type Theory (HoTT) is that the ideas of homotopy theory have very broad applicability in mathematics. Indeed, Quillen model categories comprise very general ideas that arise in a…

asked Jul 15 '13 at 14:40

François G. Dorais

43,723

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