790 research outputs found
Chern numbers and the indices of some elliptic differential operators
Libgober and Wood proved that the Chern number of a
-dimensional compact complex manifold can be determined by its Hirzebruch
-genus. Inspired by the idea of their proof, we show that, for
compact, spin, almost-complex manifolds, more Chern numbers can be determined
by the indices of some twisted Dirac and signature operators. As a byproduct,
we get a divisibility result of certain characteristic number for such
manifolds. Using our method, we give a direct proof of Libgober-Wood's result,
which was originally proved by induction.Comment: 9 pages, to appear in Pacific Journal of Mathematic
The cobordism class of the multiple points of immersions
Let f: M -> N be an even codimensional immersion between smooth manifolds. We
derive an explicit formula for the Pontrjagin numbers and signature of the
multiple point manifolds in terms of singular cohomology of M and N, the maps
induced between these by f and the characteristic classes of the normal bundle.
The main trick is to solve a recursion in cohomology by the use of
(generalized) formal power series.Comment: 17 pages; LaTeX2e document, use of eLaTeX recommended, non-standard
packages: xy, pxfonts, pbox. Accepted by Algebraic Geometry and Topology.
Corrections and clarifications mainly due to the referee of the journa
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