scholarly journals On realization of splitting obstructions in Browder-Livesay groups for closed manifold pairs

2000 ◽  
Vol 43 (1) ◽  
pp. 15-25 ◽  
Author(s):  
P. M. Akhmetiev ◽  
A. Cavicchioli ◽  
D. Repovš
Keyword(s):  
Closed Manifold ◽  
Realization Problem

AbstractWe consider some new types of realization problem for obstructions in the Browder-Livesay groups by homotopy equivalences of closed manifold pairs. We give several examples of calculations. We also consider relations with classical surgery problems.

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

scholarly journals The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles

2016 ◽  
Vol 08 (03) ◽  
pp. 545-570 ◽  
Author(s):  
Luca Asselle ◽  
Gabriele Benedetti
Keyword(s):  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Symplectic Form ◽  
Critical Value ◽  
Closed Manifold ◽  
Hamiltonian Flow ◽  
Cotangent Bundles ◽  
Almost All

Let [Formula: see text] be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian [Formula: see text] and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits for such a flow. Our main result asserts that if [Formula: see text] is not aspherical, then contractible periodic orbits exist for almost all energies above the maximum critical value of [Formula: see text].

scholarly journals A framework for the solution of the generalized realization problem

2007 ◽  
Vol 425 (2-3) ◽  
pp. 634-662 ◽  
Author(s):  
A.J. Mayo ◽  
A.C. Antoulas
Keyword(s):  
Realization Problem

A new invariant and decompositions of manifolds

2018 ◽  
Vol 27 (02) ◽  
pp. 1850019
Author(s):  
Eiji Ogasa
Keyword(s):  
Topological Invariant ◽  
The Body ◽  
Precise Definition ◽  
Closed Manifold ◽  
Compact Manifolds ◽  
Connected Components ◽  
Fixed Base

We introduce a new topological invariant [Formula: see text] of compact manifolds-with-boundaries [Formula: see text] which is much connected with boundary-unions. A boundary-union is a kind of decomposition of compact manifolds-with-boundaries. See the body of the paper for the precise definition. Let [Formula: see text] and [Formula: see text] be [Formula: see text]-dimensional compact manifolds-with-boundaries. Let [Formula: see text] be a boundary-union of [Formula: see text] and [Formula: see text]. Then we have [Formula: see text] We define [Formula: see text] as follows: First, define an invariant of [Formula: see text]-closed manifolds. Take the maximum of the invariant of all connected-components of the boundary of each handle-body of an ordered-handle-decomposition with a fixed base [Formula: see text], where we impose the condition that the base [Formula: see text] is a (not necessarily connected) closed manifold. Take the minimum of the maximum for all ordered-handle-decompositions with the base [Formula: see text]. It is our another invariant [Formula: see text]. Take the maximum of the minimum, [Formula: see text], for all basis to satisfy the above condition. It is [Formula: see text]. See the body of the paper for the precise definition.

scholarly journals Positive Partial Realization Problem for Linear Discrete-Time Systems

2007 ◽  
Vol 17 (2) ◽  
pp. 165-171 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Impulse Response ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Finite Sequence ◽  
Realization Problem ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Time Systems

Positive Partial Realization Problem for Linear Discrete-Time SystemsA partial realization problem for positive linear discrete-time systems is addressed. Sufficient conditions for the existence of its solution are established. A procedure for the computation of a positive partial realization for a given finite sequence of the values of the impulse response is proposed. The procedure is illustrated by four numerical examples.

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