Holomorphic disks and topological invariants for closed three-manifolds
´ ´ ´ By Peter Ozsvath and Zoltan Szabo*
Abstract The aim of this article is to introduce certain topological invariants for closed, oriented three-manifolds Y , equipped with a Spinc structure. Given a Heegaard splitting of Y = U0 ∪Σ U1 , these theories are variants of the Lagrangian Floer homology for the g-fold symmetric product of Σ relative to certain totally real subspaces associated to U0 and U1 . 1. Introduction Let Y be a connected, closed, oriented three-manifold, equipped with a Spin structure s. ...
Ten years ago Elsevier published the volume Recent Progress in General Topology. The
idea behind that book was to present surveys describing recent developments in most of
the primary subfields of General Topology and its applications to Algebra and Analysis.
It was our belief that the book could be of help to researchers in General Topology as a
background for the development of their own research. There were two similar predecessors,
namely, the Handbook of Set-Theoretic Topology (North Holland, Amsterdam
1984, J.E. Vaughan and K. Kunen, eds.
In the two parts of this paper we prove that the Reidemeister torsion invariants determine topological equivalence of G-representations, for G a ﬁnite cyclic group. 1. Introduction Let G be a ﬁnite group and V , V ﬁnite dimensional real orthogonal representations of G. Then V is said to be topologically equivalent to V (denoted V ∼t V ) if there exists a homeomorphism h : V → V which is G-equivariant. If V , V are topologically equivalent, but not linearly isomorphic, then such a homeomorphism is called a nonlinear similarity. ...
Let X be a projective manifold and f : X → X a rational mapping with large topological degree, dt λk−1 (f ) := the (k − 1)th dynamical degree of f . We give an elementary construction of a probability measure µf such that d−n (f n )∗ Θ → µf for every smooth probability measure Θ on X. We show t that every quasiplurisubharmonic function is µf -integrable. In particular µf does not charge either points of indeterminacy or pluripolar sets, hence µf is f -invariant with constant jacobian f ∗ µf = dt µf...
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: COMMON FIXED POINT AND INVARIANT APPROXIMATION RESULTS IN CERTAIN METRIZABLE TOPOLOGICAL VECTOR SPACES
The invariable motif for analog design is to explore the new circuit topologies, architectures and CAD technologies to overcome the design challenges coming from the new applications and new fabrication technologies. In this book, a new architecture for a SAR ADC is proposed to eliminate the process mismatches and minimize the errors.
We construct many examples of nonslice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we deﬁne a geometric ﬁltration of the 3-dimensional topological knot concordance group. The bottom part of the ﬁltration exhibits all classical concordance invariants, including the CassonGordon invariants. As a ﬁrst step, we construct an inﬁnite sequence of new obstructions that vanish on slice knots. These take values in the L-theory of skew ﬁelds associated to certain universal groups. ...
Characteristic cohomology classes, deﬁned in modulo 2 coeﬃcients by Stiefel  and Whitney  and with integral coeﬃcients by Pontrjagin , make up the primary source of ﬁrst-order invariants of smooth manifolds. When their utility was ﬁrst recognized, it became an obvious goal to study the ways in which they admitted extensions to other categories, such as the categories of topological or PL manifolds; perhaps a clean description of characteristic classes for simplicial complexes could even give useful computational techniques.
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas’s work on Π-stability. From a mathematical point of view, the most interesting feature of the deﬁnition is that the set of stability conditions Stab(D) on a ﬁxed category D has a natural topology, thus deﬁning a new invariant of triangulated categories.
Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m0 , n0 are the dimensions of the maximal lightlike subspaces tangent to M and G, respectively, where G carries any bi-invariant metric, then we have n0 ≤ m0 . We study G-actions that satisfy the condition n0 = m0 .