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1.
We give a leafwise Lefschetz theorem in the localized equivariant K-theory of a compact foliated manifold. The method is a generalization of the one adopted by M.F. Atiyah and G. Segal in the nonfoliated case. The main tool is the equivariant version of the Connes–Skandalis longitudinal index theorem for foliations. As a byproduct, we obtain a generalization of the Heitsch–Lazarov measured Lefschetz formula to arbitrary complexes with the explicit formula for the integrand, when the diffeomorphism belongs to a compact Lie group acting on the compact manifold.  相似文献   

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We construct an Abel–Jacobi mapping on the Chow group of 0-cycles of degree 0, and prove a Roitman theorem, for projective varieties over C with arbitrary singularities. Along the way, we obtain a new version of the Lefschetz Hyperplane theorem for singular varieties.  相似文献   

4.
Using the theory of Lefschetz fibrations and recent advances in mapping class group theory, surface bundles over surfaces with nonzero signature and small base genus are constructed. In particular, a genus-5 fibration over the surface of genus 26 with nonzero signature is given –- improving former results on the possible base genera for surface bundles over surfaces with nonzero signature.  相似文献   

5.
L. Katzarkov 《Acta Appl Math》2003,75(1-3):85-103
Recently, together with Auroux and Donaldson, we have introduced some new invariants of four-dimensional symplectic manifolds. Building on the Moishezon–Teicher braid factorization techniques, we show how to compute fundamental groups of compliments to a ramification curve of generic projection. We also show that these fundamental groups are only homology invariants and outline the computations in some examples.Demonstrating the ubiquity of algebra, we go further and, using Braid factorization, we compute invariants of a derived category of representations of the quiver associated with the Fukaya–Seidel category of the vanishing cycles of a Lefschetz pencil and a structure of a symplectic four-dimensional manifold. This idea is suggested by the homological mirror symmetry conjecture of Kontsevich. We do not use it in our computations, although everything is explicit. We outline a procedure for finding homeomorphic, nonsymplectomorphic, four-dimensional symplectic manifolds with the same Saiberg–Witten invariants. This procedure defines invariants in the smooth category as well.  相似文献   

6.
Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Green's functions in the Duffin–Kemmer–Petiau and Klein–Gordon–Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.  相似文献   

7.
Systems of functional–differential and functional equations occur in many biological, control and physics problems. They also include functional–differential equations of neutral type as special cases. Based on the continuous extension of the Runge–Kutta method for delay differential equations and the collocation method for functional equations, numerical methods for solving the initial value problems of systems of functional–differential and functional equations are formulated. Comprehensive analysis of the order of approximation and the numerical stability are presented.  相似文献   

8.
We consider polynomial mappings which have atypical fibres due to the asymptotic behavior at infinity. Fixing some proper extension of the polynomial mapping, we study the localizability at infinity of the variation of topology of fibres and the possibility of interpreting local results at infinity into global results. We prove local and global Bertini–Sard–Lefschetz type statements for noncompact spaces and nonproper mappings and we deduce results on the homotopy type or the connectivity of the fibres of polynomial mappings.  相似文献   

9.
The convergence and complexity of a primal–dual column generation and cutting plane algorithm from approximate analytic centers for solving convex feasibility problems defined by a deep cut separation oracle is studied. The primal–dual–infeasible Newton method is used to generate a primal–dual updating direction. The number of recentering steps is O(1) for cuts as deep as half way to the deepest cut, where the deepest cut is tangent to the primal–dual variant of Dikin's ellipsoid.  相似文献   

10.
One of the more interesting solutions of the (2+1)-dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation is the soliton solutions. We previously derived a complete group classification for the SKdV equation in 2+1 dimensions. Using classical Lie symmetries, we now consider traveling-wave reductions with a variable velocity depending on the form of an arbitrary function. The corresponding solutions of the (2+1)-dimensional equation involve up to three arbitrary smooth functions. Consequently, the solutions exhibit a rich variety of qualitative behaviors. In particular, we show the interaction of a Wadati soliton with a line soliton. Moreover, via a Miura transformation, the SKdV is closely related to the Ablowitz–Kaup–Newell–Segur (AKNS) equation in 2+1 dimensions. Using classical Lie symmetries, we consider traveling-wave reductions for the AKNS equation in 2+1 dimensions. It is interesting that neither of the (2+1)-dimensional integrable systems considered admit Virasoro-type subalgebras.  相似文献   

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