Counterexample

A long-standing conjecture due to Michael Freedman asserts that the 4-dimensional topological surgery conjecture fails for non-abelian free groups, or equivalently that a family of canonical examples of links (the generalized Borromean rings) are not A − B slice. A stronger version of the conjecture, that the Borromean rings are not even weakly A − B slice, where one drops the equivariant aspect of the problem, has been the main focus in the search for an obstruction to surgery.

21p dontetvui 17-01-2013 73 7   Download

We exhibit a counterexample to Elliott’s classification conjecture for simple, separable, and nuclear C∗ -algebras whose construction is elementary, and demonstrate the necessity of extremely fine invariants in distinguishing both approximate unitary equivalence classes of automorphisms of such algebras and isomorphism classes of the algebras themselves.

17p dontetvui 17-01-2013 71 6   Download

We investigate the relationship between an open simply-connected region Ω ⊂ S2 and the boundary Y of the hyperbolic convex hull in H3 of S2 \ Ω. A counterexample is given to Thurston’s conjecture that these spaces are related by a 2-quasiconformal homeomorphism which extends to the identity map on their common boundary, in the case when the homeomorphism is required to respect any group of M¨bius transformations which preserves Ω.

0p tuanloccuoi 04-01-2013 61 7   Download

We construct a proper C 2 -smooth function on R4 such that its Hamiltonian flow has no periodic orbits on at least one regular level set. This result can be viewed as a C 2 -smooth counterexample to the Hamiltonian Seifert conjecture in dimension four. 1. Introduction The “Hamiltonian Seifert conjecture” is the question whether or not there exists a proper function on R2n whose Hamiltonian flow has no periodic orbits on at least one regular level set.

25p tuanloccuoi 04-01-2013 58 7   Download

We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that 1) Any surface S with the same Euler number as S, and fundamental group Γ, is diffeomorphic to S. 2) The moduli space of S consists of exactly two connected components, exchanged by complex conjugation. Whence, i) On the one hand we give simple counterexamples to the DEF = DIFF question whether deformation type and diffeomorphism type coincide for algebraic surfaces. ii) On the other hand we get examples of moduli spaces without real points. iii)...

17p tuanloccuoi 04-01-2013 55 6   Download

In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Pad´ approximants e converges uniformly in compact subsets of the ball omitting poles of f . There is also apparently a cruder version of the conjecture due to Pad´ himself, going e back to the early twentieth century. We show here that for carefully chosen q on the unit circle, the Rogers-Ramanujan continued fraction 1+ qz| q 2 z| q 3 z| + + + ··· |1 |1 |1 provides a counterexample to the conjecture. We also highlight some...

44p tuanloccuoi 04-01-2013 53 7   Download

In this paper we study Lipschitz solutions of partial differential relations of the form (1) ∇u(x) ∈ K a.e. in Ω, where u is a (Lipschitz) mapping of an open set Ω ⊂ Rn into Rm , ∇u(x) is its gradient (i.e. the matrix ∂ui (x)/∂xj , 1 ≤ i ≤ m, 1 ≤ j ≤ n, defined for almost every x ∈ Ω), and K is a subset of the set M m×n of all real m × n matrices. In addition to relation (1), boundary conditions and other conditions on u will also be considered. Relation (1)...

29p tuanloccuoi 04-01-2013 52 9   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures...

9p thulanh7 04-10-2011 43 1   Download

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A counterexample to a conjecture of Erd˝s, Graham and Spencer o...

3p thulanh6 15-09-2011 51 3   Download