1
vote
0answers
21 views
Why do knot cobordisms result in functoriality with respect to knot homologies so often?
Why do knot cobordisms result in functoriality with respect to knot homologies so often?
4
votes
2answers
126 views
Are sums of the inverses of prime siblings finite?
PART I (Initial version)
Let $P$ be the set of all primes $2\ 3\ \ldots$. Let
$$P_d\ \ :=\ \ \{\ p\in P\ :\ \exists_{q\in P}\ \ 0 < |p-q|\le d\ \}$ …
6
votes
0answers
44 views
Are small knots generic?
A knot in S^3 is small if its complement does not contain a closed incompressible surface. Is it a generic property for knots, meaning that among all knots with less than $n$ cross …
13
votes
13answers
596 views
objects which can’t be defined without making choices but which end up independent of the choice
It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …
1
vote
0answers
22 views
Probability $k$ bins are non-empty.
The following problem arises in the analysis of Bloom filters.
Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …
0
votes
1answer
41 views
Interpreting numerical double integration as a matrix multiplication
I have a convex optimization problem of finding a function Q(x,y) as below:
Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the questi …
0
votes
0answers
30 views
What about weighted lens spaces (WLS) , as schemes/ algebraic varieties ?
In algebraic geometry weighted projective spaces (WPS) are very popular !
In algebraic topology , WLS have been (cohomologically at least) studied. Roughly speaking , a WPS is a …
2
votes
0answers
27 views
Quotients in Sums of Rings
Suppose we are given a commutative ring R with unit-element. Now we have a composition of R as the direct product of two rings $R\cong R_1\times R_2$. It is now straight forward, …
0
votes
0answers
27 views
Examples of intersections of two hypersurfaces with high-dimensional singular locus
I am interested in examples of hypersurfaces $X, Y$ defined by polynomials $F(x_1, \cdots, x_n), G(x_1, \cdots, x_n)$ respectively, so that the intersection $X \cap Y$ has a singul …
0
votes
0answers
46 views
Finitely-generated abelian group [closed]
Let G={(a,b) in ZxZ|a= b mod10}. Proof that G is a Finitely-generated abelian group. Find a basis of G.
2
votes
2answers
126 views
Can group solvability be detected from identities among the generators?
For $n=1$ the answer is "yes." -- A group is abelian iff its generators commute.
Let $G_0=G$ be a group and let it be generated by $X_0=X$. For each $n>0$ let $G_n=[G_{n-1},G_{n- …
-1
votes
0answers
29 views
Embedded associated prime and non zero divisor
$M$ is a finitely generated $A$-module of dimension $d$ such that $G(M)$ is eqidimensional and $M$ does not have any embedded prime.
Given $x\in I$ where $I$ is an ideal of $A$ an …
0
votes
0answers
18 views
How many geometric construction methods are there to draw the third proportional.
We know if x/y =y/z and if the straight line length for x and y are given, then how many different geometric construction methods are there to draw the straight line equals to z …
0
votes
0answers
11 views
repeated application of binomial distribution on a set of random variables
I have four solutions which are termed: A1, A2, A3, A4. These are actually the results of a searching algorithm. I know that A1 is the best solution, A2 is next to A1, A3 is next t …
3
votes
3answers
212 views
Surfaces ruled over elliptic curves
Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve.
Suppose $E$ …
