Subject: new Hopf listings Date: 13 Jul 2001 16:41:49 -0400 From: Mark Hovey To: dmd1@lehigh.edu There are 8 new papers this time. Mark Hovey New papers appearing on hopf between 6/21/01 and 7/13/01 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Hovey/relative This is the final version of the paper "Quillen model structures for relative homological algebra" by J. Daniel Christensen and Mark Hovey. There are only minor corrections and fairly major spacing changes from the previous version. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/FangF-PanJZ/cl-2-1 Title of Paper :Secondary Brown-Kervaire Quadratic forms and $\pi$-manifolds Author(s) :Fuquan Fang and Jianzhong Pan Addresses of Authors: Fuquan Fang Nankai Institute of Mathematics, Nankai University, Tianjin 300071, P.R.C email:ffang@sun.nankai.edu.cn and Jianzhong Pan Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn In this paper we assert that for each $\Phi$-oriented $2n$-manifold (c.f : Definition 1.1) $M$ where $n\ge 4$ and $n\ne 3(mod 4)$, there is a well-defined quadratic function $\phi_M: H^{n-1}(M, \Z_4)\to \Q/\Z$, we call the secondary Brown-Kervaire quadratic forms, so that \begin{itemize} \item{ $\phi _{M}(x+y)=\phi _{M}(x)+\phi _{M}(y)+j(x\cup Sq^2y)[M]$}, \item{ the Witt class of $\phi _M$ is a homotopy invariant, if the Wu class $ v_{n+2-2^i}(\nu _M)=0$ for all $i$.} \end{itemize} where $j: \Z_2 \to \Q/\Z$ is the inclusion homomorphism and $\nu _M$ the stable normal bundle of $M$. Among the applications we obtain a complete classification of $(n-2)$-connected $2n$-dimensional $\pi$-manifolds up to homeomorphism and homotopy equivalence, where $n\geq 4$ and $n+2\neq 2^i$ for any $i$. In particular, we prove that the homotopy type of such manifolds determine their homeomorphism type. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/cocat1 Title of Paper :Having the H-space structure is not a generic property Author(s) : Jianzhong Pan AMS Classification numbers :55P60,55P45 Addresses of Authors: Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn In this note, we answer in negative a question posed by McGibbon about the generic property of H-space structure. In fact we verify the conjecture of Roitberg. Incidentally, the same example also answers in negative the open problem 10 in McGibbon. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/equivar Title of Paper :Equivariant Phantom maps Author(s) : Jianzhong Pan AMS Classification numbers :55P91,55P60 Addresses of Authors: Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn A successful generalization of phantom map theory to the equivariant case for all compact Lie groups is obtained in this paper. One of the key observations is the discovery of the fact that homotopy fiber of equivariant completion splits as product of equivariant Eilenberg-Maclane spaces which seems impossible at first sight by the example of Triantafillou. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/nonneg Title of Paper :Rational homotopy theory and nonnegative curvature Author(s) : Jianzhong Pan AMS Classification numbers :53C20 53C40 55P10 Addresses of Authors: Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn In this note , we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds admit (complete) metrics with nonnegative curvature. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ-WooMH/genus2-1 Title of Paper :Mislin genus of maps Author(s) : Jianzhong Pan and Moo Ha Woo AMS Classification numbers :55D99 Addresses of Authors: Jianzhong Pan Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn and Moo Ha Woo Department of Mathematics Education , Korea University , Seoul , Korea In this paper, we prove that the Mislin genus of a (co-)H-map between (co-)H-spaces under certain natural conditions is a finite abelian group which generalizes results in Zabrodsky, McGibbon and Hurvitz 7. http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ-WooMH/phan-elem Title of Paper :Phantom elements and its Applications Author(s) : Jianzhong Pan and Moo Ha Woo AMS Classification numbers :55P10,55P60,55P62,55R10 Addresses of Authors: Jianzhong Pan Institute of Math.,Academia Sinica ,Beijing 100080 ,China email:pjz@math03.math.ac.cn and Moo Ha Woo Department of Mathematics Education , Korea University , Seoul , Korea In our previous work, a relation between Tsukiyama problem about self homotopy equivalence was found by using a generalization of phantom map. In this note , fundamental result is established for such a generalization. This is the first time one can deal with phantom maps to space not satisfying finite type condition. Application to Forgetful map is also discussed briefly. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Vavpetic-Viruel/f4at2 On the Homotopy type of the Classifying Space of the Exceptional Lie Group of Rank 4 A. VAVPETIC (ales.vavpetic@fmf.uni-lj.si) Fakulteta za Matematiko in Fiziko Univerza v Ljubljani Jadranska 19 1111 Ljubljana Slovenija and A. VIRUEL (viruel@agt.cie.uma.es) Departamento de Algebra, Geometria y Topologia Universidad de Malaga AP. 59 29080 Malaga Spain AMS Classification numbers: 55R35, 55P15 Previous work of several authors shows that the exceptional Lie group of rank 4, F_4, as a p-compact group, is determined up to isomorphism by the isomorphism type of its maximal torus normalizer for p>2. This paper considers the case p=2 proving that F_4 as 2-compact group is also determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows the authors to determine the integral homotopy type of F_4 among connected finite loop spaces with maximal tori. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://www.math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/algtop.html which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Netscape< Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to Purdue seminars, and other math related things on this page as well. The largest archive of math preprints is at http://xxx.lanl.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/new-html/submissions.html In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.