On the Lusternik-Schnirelmann category of an iterated loop space

1998 ◽  
pp. 39-41
Author(s):  
Frederick Cohen
Keyword(s):  
Loop Space ◽  
Lusternik Schnirelmann

scholarly journals Functional Band and Loop Space Maintainers in Children

2019 ◽  
Vol 2019 ◽  
pp. 1-4
Author(s):  
V. Vinothini ◽  
A. Sanguida ◽  
A. Selvabalaji ◽  
G. S. Prathima ◽  
M. Kavitha
Keyword(s):  
Clinical Application ◽  
Loop Space ◽  
Single Tooth ◽  
Space Maintainer ◽  
Space Maintenance ◽  
Band And Loop

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.

scholarly journals RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

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.

scholarly journals Morava $K$-theory and the free loop space

1992 ◽  
Vol 114 (1) ◽  
pp. 243-243
Author(s):  
John McCleary ◽  
Dennis A. McLaughlin
Keyword(s):  
Loop Space ◽  
Free Loop Space ◽  
K Theory

scholarly journals A pathological example in nonlinear spectral theory

2017 ◽  
Vol 8 (1) ◽  
pp. 707-714 ◽  
Author(s):  
Lorenzo Brasco ◽  
Giovanni Franzina
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Theory ◽  
First Eigenvalue ◽  
Open Set ◽  
Lusternik Schnirelmann ◽  
Nonlinear Spectral Theory

Abstract We construct an open set {\Omega\subset\mathbb{R}^{N}} on which an eigenvalue problem for the p-Laplacian has no isolated first eigenvalue and the spectrum is not discrete. The same example shows that the usual Lusternik–Schnirelmann minimax construction does not exhaust the whole spectrum of this eigenvalue problem.

scholarly journals Generalized loop space and TMDs

2014 ◽  
Vol 73 ◽  
pp. 02011 ◽  
Author(s):  
Tom Mertens
Keyword(s):  
Loop Space

scholarly journals Remark on the Dual EHP Sequence

1967 ◽  
Vol 29 ◽  
pp. 269-280
Author(s):  
Yasutoshi Nomura
Keyword(s):  
Loop Space ◽  
The One ◽  
Ehp Sequence

In this note we will improve the dual EHP sequence which has been constructed in [6] by showing that that can be extended by one term. We then observe that this can be used to deduce a result which has been announced by T. Ganea in [4]. As another application we will establish a theorem which asserts that, under certain conditions, a principal fibration with a loop-space as fibre is principally equivalent to the one induced by some map.

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