Detail Reidemeister torsion in generalized Morse theory Bibliografi Author: Hutchings, Michael Lounsbery ; Taubes, Clifford Henry (Advisor) Topik: MATHEMATICS Bahasa: (EN )    ISBN: 0-591-85470-8     Penerbit: Harvard University Press     Tahun Terbit: 1998     Jenis: Theses - Dissertation Fulltext: 9832393.pdf (0.0B; 0 download) Abstract We define a notion of Reidemeister torsion for the Morse theory of closed 1-forms on a finite dimensional manifold. Given a generic closed 1-form and metric, there is a Novikov complex which counts gradient flow lines between critical points. Our main new insight is that one can get a topological invariant by multiplying the algebraic Reidemeister torsion of the Novikov complex by a 'zeta function' which counts closed orbits of the gradient flow. We propose that this is the correct formalism with which to define Reidemeister torsion in Floer theory. One can use different versions of torsion; here we follow the approach to Turaev (45). In the finite dimensional case, we show that our invariant equals a version of topological Reidemesiter torsion. To do this, we first prove invariance, by analyzing the bifurications that may occur in a generic 1-parameter family, and then use this fact to compute the invariant. On a 3-manifold with $b/sp1>0,$ our invariant is conjectured to equal the Seiberg-Witten invariant, by analogy with Taube's 'SW=Gr' theorem. Assuming this conjecture, we show that the Seiberg-Witten invariant equals the topological Turaev torsion. This was conjectured by Turaev (46) and is consistent with the 'averaged' computation of the Seiberg-Witten invariants by Meng and Taubes (26). These results were obtained jointly with Yi-Jen Lee in (17, 18). I have given a somewhat different exposition here. Opini Anda Klik untuk menuliskan opini Anda tentang koleksi ini! Lihat Sejarah Pengadaan  Konversi Metadata   Kembali

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