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On Seiberg-Witten equationsοn symplectic 4-manifolds

Klaus Mohnke (1997)

Banach Center Publications

We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.

On signatures associated with ramified coverings and embedding problems

J. Wood, Emery Thomas (1973)

Annales de l'institut Fourier

Given a cohomology class ξ H 2 ( M ; Z ) there is a smooth submanifold K M Poincaré dual to ξ . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in C P n . This note summarizes some results on the question: how does the divisibility of ξ restrict the dual submanifolds K in this class ? A formula for signatures associated with a d -fold ramified cover of M branched along K is given and a proof is included in case d = 2 .

On some spaces which are covered by a product space

Izu Vaisman (1977)

Annales de l'institut Fourier

In this note, a topological version of the results obtained, in connection with the de Rham reducibility theorem (Comment. Math. Helv., 26 ( 1952), 328–344), by S. Kashiwabara (Tôhoku Math. J., 8 (1956), 13–28), (Tôhoku Math. J., 11 (1959), 327–350) and Ia. L. Sapiro (Izv. Bysh. Uceb. Zaved. Mat. no6, (1972), 78–85, Russian), (Izv. Bysh. Uceb. Zaved. Mat. no4, (1974), 104–113, Russian) is given. Thus a characterization of a class of topological spaces covered by a product space is obtained and the...

On stability of 3-manifolds

Sławomir Kwasik, Witold Rosicki (2004)

Fundamenta Mathematicae

We address the following question: How different can closed, oriented 3-manifolds be if they become homeomorphic after taking a product with a sphere? For geometric 3-manifolds this paper provides a complete answer to this question. For possibly non-geometric 3-manifolds, we establish results which concern 3-manifolds with finite fundamental group (i.e., 3-dimensional fake spherical space forms) and compare these results with results involving fake spherical space forms of higher...

On tame embeddings of solenoids into 3-space

Boju Jiang, Shicheng Wang, Hao Zheng, Qing Zhou (2011)

Fundamenta Mathematicae

Solenoids are inverse limits of the circle, and the classical knot theory is the theory of tame embeddings of the circle into 3-space. We make a general study, including certain classification results, of tame embeddings of solenoids into 3-space, seen as the "inverse limits" of tame embeddings of the circle. Some applications in topology and in dynamics are discussed. In particular, there are tamely embedded solenoids Σ ⊂ ℝ³ which are strictly achiral. Since solenoids are non-planar,...

On the AJ conjecture for cables of twist knots

Anh T. Tran (2015)

Fundamenta Mathematicae

We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.

On the connectedness of boundary and complement for domains

Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)

Annales Polonici Mathematici

This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.

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