The Chern character of ϑ-summable Fredholm modules over dg algebras and localization on loop space

Premature loss of teeth in children leads to space loss and affects arch integrity. The band and loop space maintainer is used in majority of patients requiring single tooth space maintenance in both primary and mixed dentitions. It preserves the proximal dimensions, but it is nonfunctional. This paper describes a method to modify the conventional band and loop space maintainer into a functional one and reports its clinical application and follow-up in five children.

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Blackbox computation of A ∞-algebras

Georgian Mathematical Journal ◽

10.1515/gmj.2010.005 ◽

2010 ◽

Vol 17 (2) ◽

pp. 391-404

Author(s):

Mikael Vejdemo-Johansson

Keyword(s):

Homology Theory ◽

Algebra Structure ◽

Finite Amount ◽

Computational Work ◽

Dg Algebra ◽

Dg Algebras

Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.

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The Energy Flow on the Loop Space of a Compact Lie Group

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-26.3.557 ◽

1982 ◽

Vol s2-26 (3) ◽

pp. 557-566 ◽

Cited By ~ 18

Author(s):

A. N. Pressley

Keyword(s):

Lie Group ◽

Energy Flow ◽

Loop Space ◽

Compact Lie Group

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Higher spectral flow and an entire bivariant JLO cocycle

Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology ◽

10.1017/is012008031jkt193 ◽

2012 ◽

Vol 11 (1) ◽

pp. 183-232 ◽

Cited By ~ 5

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.

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The 3-Lie algebra (2,0) tensor multiplet and equations of motion on loop space

Journal of High Energy Physics ◽

10.1007/jhep05(2011)099 ◽

2011 ◽

Vol 2011 (5) ◽

Cited By ~ 12

Author(s):

Constantinos Papageorgakis ◽

Christian Sämann

Keyword(s):

Lie Algebra ◽

Loop Space ◽

Equations Of Motion ◽

Tensor Multiplet

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RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

Glasgow Mathematical Journal ◽

10.1017/s0017089520000658 ◽

2021 ◽

pp. 1-29

Author(s):

DREW HEARD

Keyword(s):

Lie Group ◽

Loop Space ◽

Algebraic Model ◽

Compact Lie Group ◽

Loop Spaces ◽

Local Systems ◽

Special Case ◽

Finite Loop ◽

Finite Loop Space

Abstract Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree G-spectra. More generally, we show that if K is a closed subgroup of a compact Lie group G such that the Weyl group W G K is connected, then a certain category of rational G-spectra “at K” has an algebraic model. For example, when K is the trivial group, this is just the category of rational cofree G-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.

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