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On the topology and analysis of a closed one form. I (Novikov's theory revisited) | | Dan Burghelea
; Stefan Haller
; | | Date: |
5 Dec 2000 | | Subject: | Differential Geometry MSC-class: 58G26 | math.DG | | Abstract: | We consider systems $(M,omega,g)$ with $M$ a closed smooth manifold, $omega$ a real valued closed one form and $g$ a Riemannian metric, so that $(omega,g)$ is a Morse-Smale pair, Definition~2. We introduce a numerical invariant $
ho(omega,g)in[0,infty]$ and improve Morse-Novikov theory by showing that the Novikov complex comes from a cochain complex of free modules over a subring $Lambda’_{[omega],
ho}$ of the Novikov ring $Lambda_{[omega]}$ which admits surjective ring homomorphisms $ev_s:Lambda’_{[omega],
ho} oC$ for any complex number $s$ whose real part is larger than $
ho$. We extend Witten-Helffer-Sjöstrand results from a pair $(h,g)$ where $h$ is a Morse function to a pair $(omega,g)$ where $omega$ is a Morse one form. As a consequence we show that if $
ho | | Source: | arXiv, math.DG/0101043 | | Services: | Forum | Review | PDF | Favorites | |
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