tag:blogger.com,1999:blog-6555947.post110638547396188937..comments2021-02-11T23:24:26.387-07:00Comments on The Geomblog: Betti NumbersSuresh Venkatasubramanianhttp://www.blogger.com/profile/15898357513326041822noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-6555947.post-2807547878811704142007-11-19T06:19:00.000-07:002007-11-19T06:19:00.000-07:00it is simple maybe in definition but I really don'...it is simple maybe in definition but I really don't know how to calculate them for an arbitrary manifold?Do you know a book or a monograph that shows calculating them by algebraic methods?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116543599098792432005-05-19T16:59:00.000-06:002005-05-19T16:59:00.000-06:00Afra writes clearly and is 'cool' too.. reminds me...Afra writes clearly and is 'cool' too.. reminds me of Richard Feynman. Excellent color graphics. I downloaded the entire thesis !<BR/> I noticed in figure 2.6 of Topology and Computing it says radiuses. Shouldn't it be spelled radii?  <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>jurgenAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116524817113714402005-05-19T11:46:00.000-06:002005-05-19T11:46:00.000-06:00Check out Afra's web page at Stanford. His thesis ...Check out Afra's web page at Stanford. His thesis is online and the first few chapters provide a good intro to the area.  <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116513527120721462005-05-19T08:38:00.000-06:002005-05-19T08:38:00.000-06:00That intro from Topology and Computing is interest...That intro from Topology and Computing is interesting and clear. Let me know if the rest of it is as lucid. A little expensive for me, I get all my technical books from Dover publications. <BR/> <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>jurgenAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116467823639371362005-05-18T19:57:00.000-06:002005-05-18T19:57:00.000-06:00It's called 'The Road to Reality'. I highly recomm...It's called 'The Road to Reality'. I highly recommend it. I will probably post a brief review once I read it (I have it ordered), but what little I saw of it in the bookstore convinced me.<BR/><BR/>Unlike ENM, this is apurely technical book that attempts to survey the vast tracts of mathematics and physics needed to understand modern theories of physics. Any book that can make covariant derivatives make sense deserves to be bought ! <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116466883945266942005-05-18T19:41:00.000-06:002005-05-18T19:41:00.000-06:00Whats the title of the new book? I never did read...Whats the title of the new book? I never did read the Emperors New Mind. I did read the brief Penrose / Hawking book, which just posed a lot of questions. <BR/> <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A><A HREF="http://geomblog.blogspot.com/2005/01/betti-numbers_20.html" REL="nofollow" TITLE="jstuchell at verizon dot net">jurgen</A>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116462718784397362005-05-18T18:31:00.000-06:002005-05-18T18:31:00.000-06:00Good luck finding one :). I really doubt that Bett...Good luck finding one :). I really doubt that Betti numbers are amenable to easy explanations, although after reading Penrose's new book, anything is possible.  <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1116462328703725782005-05-18T18:25:00.000-06:002005-05-18T18:25:00.000-06:00Im seeking a good understandable definition of bet...Im seeking a good understandable definition of betti number and have not found one yet. It may be too abstruse to define in words. I have three<BR/>topology texts and have just ordered Intro to Topology by Bert Mendelson...perhaps there is a good defn in there but I doubt it.  <BR/><BR/><A></A><A></A>Posted by<A><B> </B></A><A HREF="http://geomblog.blogspot.com/2005/01/betti-numbers_20.html" REL="nofollow" TITLE="jstuchell at verizon dot net">jurgen</A>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1107111059653417022005-01-30T11:50:00.000-07:002005-01-30T11:50:00.000-07:00yeah yeah, rub it in :). really though, I prefer t...yeah yeah, rub it in :). really though, I prefer to read a book with some intuition in the back of my head. it helps to make the constructions a lot easier. I am working thru some books in algebraic/combinatorial topology right now. there is a nice book by Maunders(?) from Dover that I have been plowing thru. <br /><br /><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1107098861894813842005-01-30T08:27:00.000-07:002005-01-30T08:27:00.000-07:00I suppose I did the "going through topology for mo...I suppose I did the "going through topology for months" when I was young enough not to feel it much. You should go straight for a good book on Algebraic (not Combinatorial) Topology, is what I say. Then again I don't know if I'd recommend this to someone at your age (ahem!). <br /><br /><A></A><A></A>Posted by<A><B> </B></A>ACAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1106523280628144462005-01-23T16:34:00.000-07:002005-01-23T16:34:00.000-07:00well for starters, the fact that you need to go th...well for starters, the fact that you need to go thru half a book in combinatorial topology to acquire enough machinery to understand their definition. I have heard enough of "first Betti number is number of connected components, and second Betti number is number of holes..er..tunnels.. something...". I'd like something more intuitive but less rigorous so I can approach the formal definition more easily <br /><br /><A></A><A></A>Posted by<A><B> </B></A>SureshAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1106455128801765882005-01-22T21:38:00.000-07:002005-01-22T21:38:00.000-07:00What's so complicated about Betti numbers?  
...What's so complicated about Betti numbers?  <br /><br /><A></A><A></A>Posted by<A><B> </B></A>ACAnonymousnoreply@blogger.com