1,720,989 research outputs found
Sasaki structures distinguished by their basic Hodge numbers
Full text linkIn all odd dimensions we produce examples of manifolds admitting
pairs of Sasaki structures with different basic Hodge numbers. In dimension
we prove more precise results, for example we show that on connected sums of
copies of the number of Sasaki structures with different basic
Hodge numbers within a fixed homotopy class of almost contact structures is
unbounded. All the Sasaki structures we consider are negative in the sense that
the basic first Chern class is represented by a negative definite form of type
. We also discuss the relation of these results to contact topology.Comment: final version, to appear in Bull. London Math. Societ
Moser stability for locally conformally symplectic structures
No full textWe formulate and prove the analogue of Moser's stability theorem for locally conformally symplectic structures.
As special cases we recover some results previously proved by Banyaga
The geometry of symplectic pairs
No full textWe study the geometry of manifolds carrying symplectic pairs consisting of two closed -forms of constant ranks, whose kernel foliations are complementary. Using a variation of the construction of Boothby and Wang we build contact-symplectic and contact pairs from symplectic
pairs
The Geometry of Recursion Operators
No full textWe study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser’s theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geo- metric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity. For pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures. For triples we recover the notion of a hypersymplectic structure, and we also find three new structures that have not been considered before. One of these is the symplectic formulation of hyper-Kähler geometry, which turns out to be a strict generalization of the usual definition in terms of differential or Kähler geometry
Sasaki versus Kähler groups
Full text linkWe study fundamental groups of compact Sasaki manifolds and show that compared to Kähler groups, they exhibit rather different behaviour. This class of groups is not closed under taking direct products, and there is often an upper bound on the dimension of a Sasaki manifold realising a given group. The richest class of Sasaki groups arises in dimension 5
Stability Theorems for Symplectic and Contact Pairs
No full textWe prove Gray–Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one- form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan
REVIEW OF: "Kotschick D. - Neofytidis, C., On three-manifolds dominated by circle bundles, Math. Z. 274, No. 1-2, 21-32 (2013)". [DE06176500X]
No full textGiven two closed oriented n-manifolds M and N, M is said to dominate N if a non-zero degree map from
M to N exists. From dimension n = 3 on, the domination relation fails to be an ordering.
By a result of [Math. Semin. Notes, Kobe Univ. 9, 159-180 (1981; Zbl 0483.57003)], every 3-manifold turns
out to be dominated by a surface bundle over the circle; on the other hand, in [J. Lond. Math. Soc. 79 (3),
545-561 (2009; Zbl 1168.53024)] and [Groups Geom. Dyn. 7 (1), 181-204 (2013; Zbl 06147449)] it is shown
that 3-manifolds dominated by products cannot have hyperbolic or Sol3-geometry, and must often be prime.
In the present paper, the authors give a complete characterization of 3-manifolds dominated by products,
by proving that a closed oriented 3-manifold is dominated by a product if and only if it is finitely covered
either by a product or by a connected sum of copies of S2 × S1. It is worthwhile to note that the same
characterization may also be formulated in terms of Thurston geometries, or in terms of purely algebraic
properties of the fundamental group.
Moreover, the authors determine which 3-manifolds are dominated by non-trivial circle bundles, and which
3-manifold groups are presentable by products (according to [J. Lond. Math. Soc. 79 (3), 545-561 (2009;
Zbl 1168.53024)])
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