-
作者：Ginzburg, Viktor L.
摘要：We prove the Conley conjecture for a closed symplectically aspherical symplectic manifold: a Hamiltonian diffeomorphism of such a manifold has infinitely many periodic points. More precisely, we show that a Hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period. This theorem generalizes, for instance, a recent result of Hingston establishing the Conley conjecture for tori.
-
作者：Voll, Christopher
摘要：We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or J-) groups, and the normal zeta functions of J-groups of class 2. We deduce our theorem...
-
作者：Sznitman, Alain-Sol
摘要：We introduce a model of random interlacements made of a countable collection of doubly infinite paths on Z(d), d >= 3. A nonnegative parameter u measures how many trajectories enter the picture. This model describes in the large N limit the microscopic structure in the bulk, which arises when considering the disconnection time of a discrete cylinder (Z/NZ)(d-1) x Z by simple random walk, or the set of points visited by simple random walk on the discrete torus (Z/NZ)(d) at times of order uN(d)....
-
作者：van Erp, Erik
摘要：The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the principal symbol of the operator. On contact manifolds, the important Fredholm operators are not elliptic, but hypoelliptic. Their symbolic calculus is noncommutative, and is closely related to analysis on the Heisenberg group. For a hypoelliptic differential operator in the Heisenberg calculus on a cont...
-
作者：Hambly, Ben; Lyons, Terry
摘要：We introduce the notions of tree-like path and tree-like equivalence between paths and prove that the latter is an equivalence relation for paths of finite length. We show that the equivalence classes form a group with some similarity to a free group, and that in each class there is a unique path that is tree reduced. The set of these paths is the Reduced Path Group. It is a continuous analogue of the group of reduced words. The signature of the path is a power series whose coefficients are ce...
-
作者：Belolipetsky, Mikhail; Gelander, Tsachik; Lubotzky, Alexander; Shalev, Aner
摘要：We give estimates on the number AL(H)(x) of conjugacy classes of arithmetic lattices Gamma of covolume at most x in a simple Lie group H. In particular, we obtain a first concrete estimate on the number of arithmetic 3-manifolds of volume at most x. Our main result is for the classical case H = PSL(2, R) where we show that
-
作者：Laza, Radu
摘要：We characterize the image of the period map for cubic fourfolds with at worst simple singularities as the complement of an arrangement of hyperplanes in the period space. It follows then that the geometric invariant theory (GIT) compactification of the moduli space of cubic fourfolds is isomorphic to the Looijenga compactification associated to this arrangement. This paper builds on and is a natural continuation of our previous work on the GIT compactification of the moduli space of cubic four...
-
作者：Crovisier, Sylvain
摘要：We prove a conjecture of J. Palis: Any diffeomorphism of a compact manifold can be C-1-approximated by a Morse-Smale diffeomorphism or by a diffeomorphism having a transverse homoclinic intersection.
-
作者：Teleman, Andrei
摘要：We develop a general strategy, based on gauge theoretical methods, to prove existence of curves on class VII surfaces. We prove that, for b(2) = 2, every minimal class VII surface has a cycle of rational curves hence, by a result of Nakamura, is a global deformation of a one parameter family of blown up primary Hopf surfaces. The case b(2) = 1 was solved in a previous article. The fundamental object intervening in our strategy is the moduli space M-pst(0, K) of polystable bundles E with c(2)(E...
-
作者：Geisser, Thomas
摘要：We show that Bloch's complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields, finite fields, local fields of mixed characteristic, and rings of integers in number rings, generalizing results which so far have only been known for smooth schemes or in low dimensions, and unifying the p-adic and l-adic theory. As an appl...
