1,633 research outputs found
Novikov homology and non-commutative Alexander polynomials
No full textIn the early 2000' s Cochran and Harvey introduced non-commutative Alexander polynomials for 3-manifolds. Their degrees give strong lower bounds on the Thurston norm. In this paper, we make the case that the vanishing of a certain Novikov-Sikorav homology module is the correct notion of a monic non-commutative Alexander polynomial. Furthermore we will use the opportunity to give new proofs of several statements about Novikov-Sikorav homology in the three-dimensional context
Novikov homology, twisted Alexander polynomials and Thurston cones
No full text38 pages, Latex fileWe continue the study of the twisted Novikov homology, introduced in our joint paper with H.Goda (arXiv:math.DG/0312374), and its generalizations. The main applications of the developed algebraic techniques are to the topology of 3-manifolds. We show in particular that the twisted Novikov homology of a 3-manifold M of zero Euler characteristic vanishes if and only if the corresponding twisted Alexander polynomial of the fundamental group of M is monic. We discuss the relations between the Thurston norm on 1-cohomology of a three-dimensional manifold and the twisted Novikov homology of this manifold
Novikov homology, twisted Alexander polynomials and Thurston cones
No full text38 pages, Latex fileWe continue the study of the twisted Novikov homology, introduced in our joint paper with H.Goda (arXiv:math.DG/0312374), and its generalizations. The main applications of the developed algebraic techniques are to the topology of 3-manifolds. We show in particular that the twisted Novikov homology of a 3-manifold M of zero Euler characteristic vanishes if and only if the corresponding twisted Alexander polynomial of the fundamental group of M is monic. We discuss the relations between the Thurston norm on 1-cohomology of a three-dimensional manifold and the twisted Novikov homology of this manifold
On a Solution of the Optimal Stopping Problem for Processes with Independent Increments
Get PDFWe discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.
Igor Novikov et Alexander Sharov, Hubble, l'inventeur du Big Bang, 1995
No full textThomas Jean-Paul. Igor Novikov et Alexander Sharov, Hubble, l'inventeur du Big Bang, 1995. In: Raison présente, n°123, 3e trimestre 1997. Politique, nouveaux enjeux. pp. 149-151
The Novikov theory for symplectic cohomology and exact Lagrangian embeddings
Get PDFThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 121-123).Given an exact symplectic manifold, can we find topological constraints to the existence of exact Lagrangian submanifolds? I developed an approach using symplectic cohomology which provides such conditions for exact Lagrangians inside cotangent bundles and inside ALE hyperkähler spaces. For example, the only exact Lagrangians inside ALE hyperkähler spaces must be spheres. The vanishing of symplectic cohomology is an obstruction to the existence of exact Lagrangians. In the above applications even though the ordinary symplectic cohomology does not vanish, one can prove that a Novikov homology analogue for symplectic cohomology does vanish.by Alexander F. Ritter.Ph.D
Automorphic Lie algebras with dihedral symmetry
No full textThe concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl2(C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits
Banach strong Novikov conjecture for polynomially contractible groups
No full textWe prove the Banach strong Novikov conjecture for groups having polynomially bounded higher order combinatorial functions. This includes all automatic groups. (C) 2018 Elsevier Inc. All rights reserved
Strong Novikov conjecture for low degree cohomology and exotic group C{\ast}-algebras
No full textWe strengthen a result of Hanke-Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group C*-algebra holds for many other exotic group C*-algebras, in particular the one associated to the smallest strongly Morita compatible and exact crossed product functor used in the new version of the Baum-Connes conjecture. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors
CCDC 1845565: Experimental Crystal Structure Determination
No full textRelated Article: Elena Reutskaya, Angelina Osipyan, Alexander Sapegin, Alexander S. Novikov, Mikhail Krasavin|2019|J.Org.Chem.|84|1693|doi:10.1021/acs.joc.8b02805,An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
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