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MathOverflow : Recent Questions and Answers (Page 26)

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Oriented cobordism classes represented by rational homology spheres

Any homology sphere is stably parallelizable, hence nullcobordant. However, rational homology spheres need not be nullcobordant, as the example of the Wu manifold shows, which generates $text{torsion}({Omega^{text{SO}}_{5}}) cong...

Asked on 11/03/2021 by Jens Reinhold

2 answer

Tiling with similar tiles

Question 1: Is there a polygon $P$ thatcannot tile the planeandtiles the plane when copies of $P$ and some other polygon(s) all similar in shape to ...

Asked on 11/03/2021 by Nandakumar R

6 answer

Are any interesting classes of polynomial sequences besides Sheffer sequences groups under umbral composition?

This question on math.stackexchange.com has 35 views, three up-votes, and not a word from anybody, so I'm posting it here. Let us understand the term polynomial sequence to mean...

Asked on 11/03/2021

1 answer

When size matters in category theory for the working mathematician

I think a related question might be this (Set-Theoretic Issues/Categories). There are many ways in which you can avoid set theoretical paradoxes in dealing with category theory (see for...

Asked on 11/03/2021 by jg1896

4 answer

Determining the kernel of the localization map when defining the localization by generators and relations à la Serre

All rings considered will be commutative and unitary. Let $A$ be a ring, $S subseteq A$ a multiplicatively closed subset. The localization $lambda_S : A longrightarrow A[S^{-1}]$...

Asked on 11/03/2021 by MathCrawler

2 answer

Yoga on coherent flat sheaves $mathcal{F}$ over projective space $mathbb{P}^n$

I'm reading Mumfords's Lectures on Curves on an Algebraic Surface (jstor-link: https://www.jstor.org/stable/j.ctt1b9x2g3)and I found in Lecture 7 (RESUME OF THE COHOMOLOGY OF COHERENT SHEAVES ON...

Asked on 11/03/2021

1 answer

Intersection form of surface bundle over surface

Let $Sigma_g$ be a Riemannian surface of genus $g$. Let $M^4$ be a surface bundle over surface: $Sigma_g to M^4 to Sigma_h$. $Sigma_g$ is the...

Asked on 11/03/2021

1 answer

What is the order of binary partition function when number of partitions is fixed?

Given a number $N$, the number of ways to write it as a sum of powers of $2$ is called the binary partition function of $N$ and...

Asked on 11/03/2021 by Rishi Gajjala

0 answer

Solutions to $(a^c-b^c)+m(r^c-s^c)=0$ in integers

Let $cge2$ be a fixed positive integer. How many nontrivial solutions in the integers does the equation $(a^c-b^c)+3(r^c-s^c)=0$ have? If $c=2$, I think it has infinitely...

Asked on 11/03/2021

2 answer

Size of the category of cohomology theories

I'd like to understand the structure of the functor category Coh whose objects are cohomology functors from a category of Spaces to the category of graded commutative rings GCR. Spaces...

Asked on 11/03/2021

2 answer

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