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Results tagged with reference-request
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user 120914
This tag is used if a reference is needed in a paper or textbook on a specific result.
5
votes
Accepted
Cohomology of $S$-arithmetic groups with trivial coefficients such as $H^n(\rm{PGL}_2(\mathb...
This is a hard problem in general. When $N$ is not prime, then even the first homology of $\operatorname{PSL}_2(\mathbf{Z}[\frac{1}{N}])$ is non-trivial to compute (cf. Corollary 4.4 of [1]), but I re …
7
votes
Presentation of special linear group over localizations of the integers
In my recent paper (arXiv:2401.08146), I give a new presentation for $\operatorname{SL}_2(\mathbf{Z}[\frac{1}{2}])$. This group is generated by the two matrices
$$
A = \begin{pmatrix}1 & 0 \\ 1 & 1\en …
13
votes
Comparative analysis of history of mathematics
An excellent and very recent comparative analysis (which addresses your first two bullet points) on the development of infinitesimal calculus has been done by Jacques Bair, Alexandre Borovik, Vladimir …
3
votes
Origin of tropical mathematics
I asked Christian Choffrut and Dominique Perrin this question today. They essentially told me the following: certainly, the name tropical comes in honour of the Brazilian mathematician Imre Simon; and …
9
votes
1
answer
225
views
Yang-Mills algebra and lower central series of surface groups
Here is a connection that I recently noticed, but I haven't quite been able to make sense of. It might follow from well-known facts; apologies, if so. This is quite far from my area.
First, in "Yang-M …
12
votes
Accepted
Looking for an electronic copy of Holmgren's old paper
The full text of the article can be found scanned here.
8
votes
0
answers
121
views
The conjugacy problem for two-relator groups
Is the conjugacy problem for two-relator groups known to be undecidable?
The word problem for two-relator groups is a famous open problem (appearing e.g. as Question 9.29 in the Kourovka notebook), an …
2
votes
Accepted
Algorithms for Polynomials Over a Real Algebraic Number Field, a reference
The thesis can be found here.
10
votes
Which great mathematicians had great political commitments?
How about a very recent political appointment? Eric Lander co-chaired Obama's "Council of Advisors on Science and Technology", and was very recently appointed to President Biden's director of the Offi …
1
vote
Surveys on unknotting number
Lackenby discussed the unknotting number (and mentions some explicit knots for which we do not know the unknotting number!) in
Lackenby, Marc, Elementary knot theory, Woodhouse, N. M. J. (ed.), Lectur …
3
votes
Which groups are LERF?
Polycyclic groups are LERF, by Mal'cev 1948. In particular, all nilpotent and all abelian groups are LERF.
As mentioned in the comments, as not all one-relator groups are residually finite, not all on …
11
votes
Accepted
Reference request: Recent progress on the conjugacy problem for torsion-free one-relator gro...
As mentioned in the comments, this is still considered an open problem. I thought I'd flesh out a few aspects. A solution was claimed in 1992 by Juhasz, but it seems to have failed to convince experts …
11
votes
Atlas-like websites on specific areas of mathematics
The Blocks of Finite Groups wiki, which aims to classify the Morita equivalence classes of blocks with a given defect group. This is in part to understand Donovan's Conjecture better.
34
votes
What are examples of (collections of) papers which "close" a field?
This is not, perhaps, a very large area, nor a complete "ending", but it was an interesting development in early semigroup theory that I think bears writing down.
Some background, first. A semigroup $ …
4
votes
super Lyndon words
An article you probably want to look at is E. S. Chibrikov, "The Right-Normed Basis for a Free Lie Superalgebra and Lyndon–Shirshov Words", Algebra Logika 45 (2006), issue 4, pp. 458--483. This contai …