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  • Bounds on genus and geometric intersections from cylindrical end moduli spaces
    Strle, Sašo
    We present a way of computing a lower bound for the genus of any smooth representative of a homology class of positive self-intersection in a smooth four-manifold ▫$X$▫ with second positive Betti ... number ▫$b_2^+(X) = 1$▫. We study the solutions of the Seiberg-Witten equations on the cylindrical end manifold which is the complement of the surface representing the class. The result can be formulated as a form of generalized adjunction inequality. The bounds obtained depend only on the rational homology type of the manifold, and include the Thom conjecture as a special case. We generalize this approach to derive lower bounds on the number of intersection points of ▫$n$▫ algebraically disjoint surfaces of positive self-intersection of manifolds with ▫$b_2^+(X) = n$▫.
    Vir: Journal of differential geometry. - ISSN 0022-040X (Vol. 65, no. 3, 2003, str. 469-511)
    Vrsta gradiva - članek, sestavni del
    Leto - 2003
    Jezik - angleški
    COBISS.SI-ID - 13135193

vir: Journal of differential geometry. - ISSN 0022-040X (Vol. 65, no. 3, 2003, str. 469-511)

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