scholarly journals On Stacked Triangulated Manifolds

10.37236/6181 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Basudeb Datta ◽  
Satoshi Murai
Keyword(s):  
Connected Manifold

We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension $d \geq 4$, if $\Delta$ is a tight connected closed homology $d$-manifold whose $i$th homology vanishes for $1 < i < d-1$, then $\Delta$ is a stacked triangulation of a manifold. These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger. 

scholarly journals Projective Connections and Projective Transformations

1957 ◽  
Vol 12 ◽  
pp. 1-24 ◽  
Author(s):  
Noboru Tanaka
Keyword(s):  
Affine Transformations ◽  
Connected Manifold ◽  
Projective Transformations

The main purpose of the present paper is to establish a theorem concerning the relation between the group of all projective transformations on an affinely connected manifold and the group of all affine transformations.

scholarly journals Yang–Mills theory and jumping curves

2015 ◽  
Vol 26 (05) ◽  
pp. 1550029
Author(s):  
Yasha Savelyev
Keyword(s):  
Vector Bundle ◽  
Holomorphic Vector Bundle ◽  
Chain Complex ◽  
Complex Manifolds ◽  
Smooth Manifolds ◽  
Hermitian Vector Bundle ◽  
Connected Manifold ◽  
Classical Sense ◽  
Yang Mills ◽  
Simply Connected

We study a smooth analogue of jumping curves of a holomorphic vector bundle, and use Yang–Mills theory over S2 to show that any non-trivial, smooth Hermitian vector bundle E over a smooth simply connected manifold, must have such curves. This is used to give new examples complex manifolds for which a non-trivial holomorphic vector bundle must have jumping curves in the classical sense (when c1(E) is zero). We also use this to give a new proof of a theorem of Gromov on the norm of curvature of unitary connections, and make the theorem slightly sharper. Lastly we define a sequence of new non-trivial integer invariants of smooth manifolds, connected to this theory of smooth jumping curves, and make some computations of these invariants. Our methods include an application of the recently developed Morse–Bott chain complex for the Yang–Mills functional over S2.

Local cohomology of the algebra of C ∞ functions on a connected manifold

1980 ◽  
Vol 4 (3) ◽  
pp. 157-167 ◽  
Author(s):  
M. Cahen ◽  
S. Gutt ◽  
M. De Wilde
Keyword(s):  
Local Cohomology ◽  
Connected Manifold

scholarly journals In simply connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hiro Lee Tanaka
Keyword(s):  
Connected Manifold ◽  
Cotangent Bundles ◽  
Lagrangian Cobordisms ◽  
Simply Connected ◽  
Lagrangian Cobordism

Abstract Let Q be a simply connected manifold. We show that every exact Lagrangian cobordism between compact, exact Lagrangians in T*Q is an h-cobordism. This is a corollary of the Abouzaid–Kragh Theorem.

A Note on Involutions with a Finite Number of Fixed Points

1968 ◽  
Vol 20 ◽  
pp. 1522-1530
Author(s):  
John D. Miller
Keyword(s):  
Finite Number ◽  
Fixed Points ◽  
Connected Manifold ◽  
Simply Connected

LetMbe a smooth, closed, simply connected manifold of dimension greater than 5. LetTbe an involution onMwith a positive, finite number of fixed points. Our aim in this paper is to prove the following theorem (which is somewhat like that of Wasserman (7)).

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Grzegorz Graff ◽  
Agnieszka Kaczkowska
Keyword(s):  
Natural Number ◽  
Homotopy Class ◽  
Periodic Points ◽  
Topological Invariant ◽  
Periodic Sequence ◽  
Connected Manifold ◽  
Lefschetz Numbers ◽  
Simply Connected Manifolds ◽  
Simply Connected

AbstractLet f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f.In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

On the number of caustics for invariant tori of Hamiltonian systems with two degrees of freedom

1991 ◽  
Vol 11 (2) ◽  
pp. 273-278 ◽  
Author(s):  
Misha Bialy
Keyword(s):  
Hamiltonian Systems ◽  
Cotangent Bundle ◽  
Degrees Of Freedom ◽  
Invariant Tori ◽  
Hamiltonian Function ◽  
Canonical Projection ◽  
Classical Type ◽  
Two Dimensional ◽  
Hamiltonian Flow ◽  
Connected Manifold

Let X be a two-dimensional orientable connected manifold without boundary, H: T*X → ℝ a smooth hamiltonian function denned on the cotangent bundle. We will assume that H is of a ‘classical type’ that is convex and even on each fibre Tx*X. The goal of this paper is to describe the set Γ of all singular points of the projection Θ|L where ι: L → T*X is a smooth embedded 2-torus invariant under the hamiltonian flow h1, Θ: T*X → X is the canonical projection.

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