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Using a covariant description of the geometry of deformations for extendons,it is shown that the topological corrections for the string action associatedwith the Euler characteristic and the first Chern number of the normal bundleof the worldsheet, although do not give dynamics to the string, modify thesymplectic properties of the covariant phase space of the theory. Futureextensions of the present results are outlined.Comment: 12 page

The Euler characteristic and the first Chern number in the covariant phase space formulation of string theory