Subject: new Hopf listings From: Mark Hovey Date: 04 Apr 1998 06:50:59 +0000 ------------------------------------ Four new papers this time--one at Hopf and three at xxx. Mark Hovey New papers uploaded to Hopf and xxx between 3/25/98 and 4/4/98: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Crossley-Whitehouse/conjinvs Title: On Conjugation Invariants in the dual Steenrod algebra Authors: M. D. Crossley and Sarah Whitehouse AMS Classification Numbers: 55S10 Address (of both authors): Departement de Mathematiques, Institut Galilee, Universite Paris 13, 93430 Villetaneuse, France. Email addresses: crossley@math.univ-paris13.fr sarah@math.univ-paris13.fr Abstract Text: We investigate the canonical conjugation, chi, of the mod 2 dual Steenrod algebra A_*, with a view to determining the subspace, A_*^chi, of elements invariant under chi. We give bounds on the dimension of this subspace for each degree and show that, after inverting xi_1, it becomes polynomial on a natural set of generators. 2. http://xxx.lanl.gov/dvi/math.DG/9803136 (This paper is cross-listed in the algebraic topology and differential geometry sections of xxx, as is the next one.) From: Michael Farber Date: Fri, 27 Mar 1998 16:34:26 GMT (23kb) Title: Witten deformation and polynomial differential forms Authors: Michael Farber and Eugenii Shustin Comments: 27 pages, 4 figures, AmsTex Subj-class: Differential Geometry; Algebraic Topology \\ As is well-known, the Witten deformation of the De Rham complex computes the De Rham cohomology. In this paper we study the Witten deformation on a noncompact manifold and restrict it to differential forms which behave polynomially near infinity. Such polynomial differential forms naturally appear on manifolds with a cylindrical structure. We prove that the cohomology of the Witten deformation acting on the complex of the polynomially growing forms can be computed as the relative cohomology of the manifold with respect to the negative remote fiber of the function. We show that the assumptions of our main theorem are satisfied in a number of interesting special cases, including generic real polynomials. 3. http://xxx.lanl.gov/dvi/math.DG/9803137 From: Michael Farber Date: Fri, 27 Mar 1998 16:48:58 GMT (27kb) Title: Poincar\'e - Reidemeister metric, Euler structures, and torsion Authors: Michael Farber and Vladimir Turaev Comments: 3 figures, AmsTex Subj-class: Differential Geometry; Algebraic Topology \\ In this paper we define a Poincar\'e-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial "torsion-type" invariant which refines the PR-metric, introduced earlier by the first author, and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler structures, introduced earlier by the second author. We show that the sign of our PR-scalar product is determined by the Stiefel-Whitney classes and the semi-characteristic of the manifold. As an application, we compute the Ray-Singer analytic torsion via the torsions of Euler structures. Another application: a computation of the twisted semi-characteristic in terms of the Stiefel-Whitney classes. 4. http://xxx.lanl.gov/dvi/math.AT/9803156 From: Jim Stasheff Date: Tue, 31 Mar 1998 20:12:53 GMT (11kb) Title: Grafting Boardman's Cherry Trees to Quantum Field Theory Authors: Jim Stasheff Comments: 8 pages, 9 figures Subj-class: Algebraic Topology; Quantum Algebra \\ Michael Boardman has been a major contributor to the theory of infinite loop spaces and higher homotopy algebra. Indeed Boardman was the first to refer to `homotopy everything'. One particular contribution which has had major progeny is his use of `geometric' trees, combinatorial tress with lengths attached to edges. Here is a modified version of the talk given to honor Mike on the occassion of his 60th birthday. It is an idiosyncratic survey of parts of homotopy algebra from Poincar\'e to the present day, with emphasis on Boardman's original ideas, starting with his cubical subdivision of the associahedra through recent applications in mathematical physics via compactifications of moduli spaces. ---------------------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.cs.wesleyan.edu/Math/Guests/Mark If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/public/www-data/algtop.html , which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. The general xxx archive URL is http://xxx.lanl.gov. More useful is the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu You can also use 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/pub/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. For instructions on uploading papers to xxx, see http://front.math.ucdavis.edu I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive. ------- End of forwarded message ------- ------- End of forwarded message -------