scholarly journals Von Neumann rho invariants and torsion in the topological knot concordance group

2012 ◽  
Vol 12 (2) ◽  
pp. 753-789 ◽  
Author(s):  
Christopher William Davis
Keyword(s):  
Von Neumann ◽  
Knot Concordance

scholarly journals Knot concordance and von Neumann $\rho$ -invariants

2007 ◽  
Vol 137 (2) ◽  
pp. 337-379 ◽  
Author(s):  
Tim D. Cochran ◽  
Peter Teichner
Keyword(s):  
Von Neumann ◽  
Knot Concordance

scholarly journals Knots having the same Seifert form and primary decomposition of knot concordance

2017 ◽  
Vol 26 (14) ◽  
pp. 1750103
Author(s):  
Taehee Kim
Keyword(s):  
Infinite Family ◽  
Alexander Polynomial ◽  
Primary Decomposition ◽  
Amenable Groups ◽  
Von Neumann ◽  
Knot Concordance ◽  
Linearly Independent

We show that for each Seifert form of an algebraically slice knot with nontrivial Alexander polynomial, there exists an infinite family of knots having the Seifert form such that the knots are linearly independent in the knot concordance group and not concordant to any knot with coprime Alexander polynomial. Key ingredients for the proof are Cheeger–Gromov–von Neumann [Formula: see text]-invariants for amenable groups developed by Cha–Orr and polynomial splittings of metabelian [Formula: see text]-invariants.

scholarly journals Primary decomposition of knot concordance and von Neumann rho-invariants

2020 ◽  
Vol 149 (1) ◽  
pp. 439-447
Author(s):  
Min Hoon Kim ◽  
Se-Goo Kim ◽  
Taehee Kim
Keyword(s):  
Primary Decomposition ◽  
Von Neumann ◽  
Knot Concordance

Lectures on von Neumann Algebras

2019 ◽  
Author(s):  
Serban-Valentin Stratila ◽  
Laszlo Zsido
Keyword(s):  
Von Neumann Algebras ◽  
Von Neumann

John von Neumann

2004 ◽  
Vol 174 (12) ◽  
pp. 1371 ◽  
Author(s):  
Mikhail I. Monastyrskii
Keyword(s):  
John Von Neumann ◽  
Von Neumann

Information mechanics

2017 ◽  
Author(s):  
Sandip Tiwari
Keyword(s):  
Information Flow ◽  
Irreversible Processes ◽  
State Machines ◽  
Science And Engineering ◽  
Von Neumann ◽  
Principle Of Maximum Entropy ◽  
Information Manipulation ◽  
Classical Quantum ◽  
Physical Laws ◽  
Principle Of Maximum

Information is physical, so its manipulation through devices is subject to its own mechanics: the science and engineering of behavioral description, which is intermingled with classical, quantum and statistical mechanics principles. This chapter is a unification of these principles and physical laws with their implications for nanoscale. Ideas of state machines, Church-Turing thesis and its embodiment in various state machines, probabilities, Bayesian principles and entropy in its various forms (Shannon, Boltzmann, von Neumann, algorithmic) with an eye on the principle of maximum entropy as an information manipulation tool. Notions of conservation and non-conservation are applied to example circuit forms folding in adiabatic, isothermal, reversible and irreversible processes. This brings out implications of fluctuation and transitions, the interplay of errors and stability and the energy cost of determinism. It concludes discussing networks as tools to understand information flow and decision making and with an introduction to entanglement in quantum computing.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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