Sometimes an anonymous review is “a tale told by an idiot …”

… “full of sound and fury, signifying nothing.” And the editor believes it, even if it is self-contradictory, after sitting on the article for half a year.

There are two problems:

  • the problem of time; you write a long and dense article, which may be hard to review and the referee, instead of declining to review it, it keeps it until the editor presses him to write a review, then he writes some fast, crappy report, much below the quality of the work required.
  • the problem of communication: there is no two way communication with the author. After waiting a considerable amount of time, the author has nothing else to do than to re-submit the article to another journal.

Both problems could be easily solved by open peer-review. See Open peer-review as a service.

The referee can well be anonymous, if he wishes, but a dialogue with the author and, more important, with other participants could only improve the quality of the review (and by way of consequence, the quality of the article).

I reproduce further such a review, with comments. It is about the article “Sub-riemannian geometry from intrinsic viewpoint” arXiv:1206.3093 .  You don’t need to read it, maybe excepting the title, abstract and contents pages, which I reproduce here:

Sub-riemannian geometry from intrinsic viewpoint
Marius Buliga
Institute of Mathematics, Romanian Academy
P.O. BOX 1-764, RO 014700
Bucuresti, Romania
Marius.Buliga@imar.ro
This version: 14.06.2012

Abstract

Gromov proposed to extract the (differential) geometric content of a sub-riemannian space exclusively from its Carnot-Caratheodory distance. One of the most striking features of a regular sub-riemannian space is that it has at any point a metric tangent space with the algebraic structure of a Carnot group, hence a homogeneous Lie group. Siebert characterizes homogeneous Lie groups as locally compact groups admitting a contracting and continuous one-parameter group of automorphisms. Siebert result has not a metric character.
In these notes I show that sub-riemannian geometry may be described by about 12 axioms, without using any a priori given differential structure, but using dilation structures instead.
Dilation structures bring forth the other intrinsic ingredient, namely the dilations, thus blending Gromov metric point of view with Siebert algebraic one.
MSC2000: 51K10, 53C17, 53C23

1 Introduction       2
2 Metric spaces, groupoids, norms    4
2.1 Normed groups and normed groupoids      5
2.2 Gromov-Hausdorff distance     7
2.3 Length in metric spaces       8
2.4 Metric profiles. Metric tangent space      10
2.5 Curvdimension and curvature     12

3 Groups with dilations      13
3.1 Conical groups     14
3.2 Carnot groups     14
3.3 Contractible groups   15

4 Dilation structures  16
4.1 Normed groupoids with dilations     16
4.2 Dilation structures, definition    18

5 Examples of dilation structures 20
5.1 Snowflakes, nonstandard dilations in the plane    20
5.2 Normed groups with dilations    21
5.3 Riemannian manifolds    22

6 Length dilation structures 22
7 Properties of dilation structures    24
7.1 Metric profiles associated with dilation structures    24
7.2 The tangent bundle of a dilation structure    26
7.3 Differentiability with respect to a pair of dilation structures    29
7.4 Equivalent dilation structures     30
7.5 Distribution of a dilation structure     31

8 Supplementary properties of dilation structures 32
8.1 The Radon-Nikodym property    32
8.2 Radon-Nikodym property, representation of length, distributions     33
8.3 Tempered dilation structures    34
9 Dilation structures on sub-riemannian manifolds   37
9.1 Sub-riemannian manifolds    37
9.2 Sub-riemannian dilation structures associated to normal frames     38

 

10 Coherent projections: a dilation structure looks down on another   41
10.1 Coherent projections     42
10.2 Length functionals associated to coherent projections    44
10.3 Conditions (A) and (B)     45

11 Distributions in sub-riemannian spaces as coherent projections    45
12 An intrinsic description of sub-riemannian geometry    47
12.1 The generalized Chow condition     47
12.2 The candidate tangent space    50
12.3 Coherent projections induce length dilation structures  53

Now the report:

 

Referee report for the paper


 Sub-riemannian geometry from intrinsic viewpoint

Marius Buliga
for

New York Journal of Mathematics (NYJM).

One of the important theorems in sub-riemannian geometry is a result
credited to Mitchell that says that Gromov-Hausdorff metric tangents
to sub-riemannian manifolds are Carnot groups.
For riemannian manifolds, this result is an exercise, while for
sub-riemannian manifolds it is quite complicate. The only known
strategy is to define special coordinates and using them define some
approximate dilations. With this dilations, the rest of the argument
becomes very easy.
Initially, Buliga isolates the properties required for such dilations
and considers
more general settings (groupoids instead of metric spaces).
However, all the theory is discussed for metric spaces, and the
groupoids leave only confusion to the reader.
His claims are that
1) when this dilations are present, then the tangents are Carnot groups,
[Rmk. The dilations are assumed to satisfy 5 very strong conditions,
e.g., A3 says that the tangent exists - A4 says that the tangent has a
multiplication law.]
2) the only such dilation structures (with other extra assumptios) are
the riemannian manifolds.
He misses to discuss the most important part of the theory:
sub-riemannian manifolds admit such dilations (or, equivalently,
normal frames).
His exposition is not educational and is not a simplification of the
paper by Mitchell (nor of the one by Bellaiche).




The paper is a cut-and-past process from previous papers of the
author. The paper does not seem reorganised at all. It is not
consistent, full of typos, English mistakes and incomplete sentences.
The referee (who is not a spellchecker nor a proofread) thinks that
the author himself could spot plenty of things to fix, just by reading
the paper (below there are some important things that needs to be
fixed).


The paper contains 53 definitions – fifty-three!.
There are 15 Theorems (6 of which are already present in other papers
by the author of by other people. In particular 3 of the theorems are
already present in [4].)
The 27 proofs are not clear, incomplete, or totally obvious.

The author consider thm 8.10 as the main result. However, after
unwrapping the definitions, the statement is: a length space that is
locally bi-lipschitz to a commutative Lie group is locally
bi-lipschitz to a Riemannian manifold. (The proof refers to Cor 8.9,
which I was unable to judge, since it seems that the definition of
“tempered” obviously implies “length” and “locally bi-lipschitz to the
tangent”)


The author confuses the reader with long definitions, which seems very
general, but are only satisfied by sub-riemannian manifolds.
The definitions are so complex that the results are tautologies, after
having understood the assumptions. Indeed, the definitions are as long
as the proofs. Just two examples: thm 7.1 is a consequence of def 4.4,
thm 9.9 is a consequence of def 9.7.

Some objects/notions are not defined or are defined many pages after
they are used.



Small remarks for the author:

def 2.21 is a little o or big O?


page 13 line 2. Which your convention, the curvdim of a come in infinite.
page 13 line -2. an N is missing in the norm


page 16 line 2, what is \nu?

prop 4.2 What do you mean with separable norm?

page 18 there are a couple of “dif” which should be fixed.
in the formula before (15), A should be [0,A]

pag 19 A4. there are uncompleted sentences.

Regarding the line before thm 7.1, I don’t agree that the next theorem
is a generalisation of Mitchell’s, since the core of his thm is the
existence of dilation structures.

Prop 7.2 What is a \Gamma -irq

Prop 8.2 what is a geodesic spray?

Beginning of sec 8.3 This is a which -> This is a

Beginning of sec 9 contains a lot of English mistakes.

Beginning of sec 9.1 “we shall suppose that the dimension of the
distribution is globally constant..” is not needed since the manifold
is connected

thm 9.2 rank -> step

In the second sentence of def 9.4, the existence of the orthonormal
frame is automatic.

 

Now, besides some of the typos, the report is simply crap:

  • the referee complains that I’m doing it for groupoids, then says that what I am doing applies only to subriemannian spaces.
  • before, he says that in fact I’m doing it only for riemannian spaces.
  • I never claim that there is a main result in this long article, but somehow the referee mentions one of the theorems as the main result, while I am using it only as an example showing what the theory says in the trivial case, the one of riemannian manifolds.
  • the referee says that I don’t treat the sub-riemannian case. Should decide which is true, among the various claims, but take a look at the contents to get an opinion.
  • I never claim what the referee thinks are my two claims, both being of course wrong,
  • in the claim 1) (of the referee) he does not understand that the problem is not the definition of an operation, but the proof that the operation is a Carnot group one (I pass the whole story that in fact the operation is a conical group one, for regular sub-riemannian manifolds this translates into a Carnot group operation by using Siebert, too subtle for the referee)
  • the claim 2) is self-contradictory just by reading only the report.
  • 53 definitions (it is a very dense course), 15 theorems and 27 proofs, which are with no argument: “ not clear, incomplete, or totally obvious
  • but he goes on hunting the typos, thanks, that’s essential to show that he did read the article.

There is a part of the text which is especially perverse: The paper is a cut-and-past process from previous papers of the
author.

Mind you, this is a course based on several papers, most of them unpublished! Moreover, every contribution from previous papers is mentioned.

Tell me what to do with these papers: being unpublished, can I use them for a paper submitted to publication? Or else, they can be safely ignored because they are not published? Hmm.

This shows to me that the referee knows what I am doing, but he does not like it.

Fortunately, all the papers, published or not, are available on the arXiv with the submission dates and versions.

 

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See also previous posts:

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4 thoughts on “Sometimes an anonymous review is “a tale told by an idiot …””

  1. You can see from the review that the guy contradicts himself, several times, and from the end of the review you can infer that that’s nothing wrong which causes his blindness, other than bad intent fueled by old resentments (because I have not fall over in front of the grandeur of some institutions, as I should have done as a young Romanian barbarian). The editor trusts him because he is a good mathematician and because he does not have time for this drama stuff. All this is an example of failure of communication. Many things could go much better for everyone without all this stuff.

  2. Hwaaa… that’s horrible!!!
    Maybe you can revise the paper, then send the editor an e-mail together with the revised paper, rebutting the referee’s claims, to convince the editor to send the revised version straight back to the same referee for reconsideration. I suspect it will go much more quickly this time around, because the referee has already had the opportunity to look at it.

    1. Thanks! I’m used to this, probably will transform it into a monograph. The SR geometry is in fact the poor man version of non-commutative analysis :) The referee clearly does not want to understand that and the review is misleading in almost all aspects.
      But there is a huge potential in SR geometry if you look at it as just an example of a new general phenomenon, like say the half-space model of hyperbolic geometry compared to hyperbolic geometry.
      You have all: a very concrete example of (a kind of a) differential structure not based on the atlasses idea (so good bye local=infinitesimal and sheaves), a fractal space from the metric pov which is also smooth wrt to this more general structure, non-commutative groups with dilations instead of modules (or vector spaces).
      It is somehow very physics like, especially the fact that it can be used as a model for spaces which are topologically trivial, but nevertheless very different at different scales.
      A gem! After people will get fed up with Alexandrov spaces, they will pass to these.

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