A new construction of 6-manifolds

This paper provides a topological method to construct all simply-connected, spin, smooth 6-manifolds with torsion-free homology using simply-connected, smooth 4-manifolds as building blocks. We explicitly determine the invariants that classify these 6-manifolds from the intersection form and specific homology classes of the 4-manifold building blocks.


Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01)
We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications
Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
A generalisation of the Morse inequalities
Bhupal, Mohan Lal (Cambridge University Press (CUP), 2001-06-01)
In this paper we construct a family of variational families for a Legendrian embedding, into the 1-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embeddings, by discretising the action functional. We compute the second variation of a generating function obtained as above at a nondegenerate critical point and prove a formula relating the signature of the second variation to the Maslov index as the mesh goes to zero. We use this to prove a generalisation of the ...
Intelligent analysis of chaos roughness in regularity of walk for a two legged robot
Kaygisiz, BH; Erkmen, İsmet; Erkmen, Aydan Müşerref (Elsevier BV, 2006-07-01)
We describe in this paper a new approach to the identification of the chaotic boundaries of regular (periodic and quasiperiodic) regions in nonlinear systems, using cell mapping equipped with measures of fractal dimension and rough sets. The proposed fractal-rough set approach considers a state space divided into cells where cell trajectories are determined using cell to cell mapping technique. All image cells in the state space, equipped with their individual fractal dimension are then classified as being ...
Differential quadrature solution of nonlinear reaction-diffusion equation with relaxation-type time integration
Meral, G.; Tezer, Münevver (Informa UK Limited, 2009-01-01)
This paper presents the combined application of differential quadrature method (DQM) and finite-difference method (FDM) with a relaxation parameter to nonlinear reaction-diffusion equation in one and two dimensions. The polynomial-based DQM is employed to discretize the spatial partial derivatives by using Gauss-Chebyshev-Lobatto points. The resulting system of ordinary differential equations is solved, discretizating the time derivative by an explicit FDM. A relaxation parameter is used to position the sol...
Citation Formats
A. Beyaz, “A new construction of 6-manifolds,” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 4409–4424, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45845.