Postnikov's books on Differential Geometry.

[Maria V. Albornoz]

Dear all,

I have found that some person is selling a set of six books on
Differential Geometry by Postnikov on eBay for about $100. I am interested
in the topic but I do not know the books.

This person claims the books to be comparable to those of Kobayashi Nomizu
or Spivak, but I am unsure. Do you know anything about the quality of
those books? Do you know how they compare to the ones above?

Also, Postnikov has a book on Springer, Geometry VI, that sells for 99.00
and I do not know if it is connected to the others in some sense or not,
appart from being from the same author. Are they a continuation? Or is it
based on the previous ones?

Please, advise. I do not know what to do about those books.

Regards,

MV

[Lieven Marchand]

I have four books by Postnikov in a French translation:

* Geometrie analytique
* Varietes differentiables
* Geometrie differentielle
* Groupes et algebres de Lie

Assuming you're talking about the same series, they're nice. It's the
notes of a lecture course at a Moscow university taking students from
very elementary analytic geometry to graduate level differential
geometry. The exposition is careful and self contained. It also aims
to be complete, sometimes a bit in the extreme. In the book on
manifolds, he spends a lecture deriving enough algebraic topology to
prove that the dimension of a manifold is unique, instead of absorbing
this in the definition.

Some of his definitions are a bit unusual or different from the
Western ones. For instance, in the definition of a manifold, it's
customary to start with a topological space and require the charts to
be continous. He induces the topology from the given charts.

--
Lieven Marchand <m...@wyrd.be>
She says, "Honey, you're a Bastard of great proportion."
He says, "Darling, I plead guilty to that sin."
Cowboy Junkies -- A few simple words

[Marko]

I have not heard of this books but a well known series of books by
M.M. Postnikov is "Lectures in geometry"

First book (Semester 1) is Analytic geometry.
Second book (Semester 2) is Linear Algebra and Differential Geometry
Third -||- is Smooth Mainfolds
Fourth -||- is Differential Geometry
Fifth -||- is Lie groups and Lie algebras

Don't know if there is a sixth volume.

These book have been translated into French, Spanish.

I have read only first one but I guess that other are just as good, it
got good reviews check it yourself in Mathematical Reviews:
http://www.ams.org/mathscinet

"Maria V. Albornoz" <mval...@artsci.wustl.edu> wrote in message news:<Pine.GSO.4.31.02021...@ascc.artsci.wustl.edu>...

[Predrag Stojkov, Ph.D.]

Maria,

I do not know if those are the same books that I know.
I had once, more than ten years ago, the set of M. Postnikov books (in
Russian) on Various geometrical issues. As I remember, only one volume was
on differential geometry (others were on analytical geometry, Lee groups,
etc...). They were designed to serve as textbooks for the complete set of
courses (5-6 semesters) in geometry at the introductory (russian level, not
american) university level. So, first couple of volumes were relative simple
(to me, then), but later ones were challenging. I learned a lot from them,
and one day will buy them again (am still sorry that I do not have these
books anymore).

Huh. Is that any useful recommendation?

Predrag Stojkov

"Maria V. Albornoz" <mval...@artsci.wustl.edu> wrote in message
news:Pine.GSO.4.31.02021...@ascc.artsci.wustl.edu...

[Robert Low]

On 19 Feb 2002, Marko wrote:

> I have not heard of this books but a well known series of books by
> M.M. Postnikov is "Lectures in geometry"
>
> First book (Semester 1) is Analytic geometry.
> Second book (Semester 2) is Linear Algebra and Differential Geometry
> Third -||- is Smooth Mainfolds
> Fourth -||- is Differential Geometry
> Fifth -||- is Lie groups and Lie algebras
>
> Don't know if there is a sixth volume.

Sixth is Riemannian geometry. Assumes quite a lot of background:
if you don't already know about manifolds, connections
on vector bundles, Lie groups and classical differential
geometry, it's probably worth getting to grips
with some of that first. It seems plausible (though I haven't
seen them, I'm going by the titles) that the first five books
provide the required background.

---
Rob. http://www.mis.coventry.ac.uk/~mtx014/