scholarly journals On Spaces with Vanishing Low-Dimensional Homotopy Groups

1948 ◽  
Vol 34 (5) ◽  
pp. 207-211 ◽  
Author(s):  
G. W. Whitehead
Keyword(s):  
Homotopy Groups ◽  
Low Dimensional

scholarly journals HOMOTOPY GROUPS OF MODULI SPACES OF STABLE QUIVER REPRESENTATIONS

2010 ◽  
Vol 21 (09) ◽  
pp. 1219-1238
Author(s):  
GRAEME WILKIN
Keyword(s):  
Euclidean Space ◽  
Moduli Space ◽  
Moduli Spaces ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Homotopy Groups ◽  
Quiver Representations ◽  
Dimension Vector ◽  
Fixed Dimension ◽  
Low Dimensional

The purpose of this paper is to describe a method for computing homotopy groups of the space of α-stable representations of a quiver with fixed dimension vector and stability parameter α. The main result is that the homotopy groups of this space are trivial up to a certain dimension, which depends on the quiver, the choice of dimension vector, and the choice of parameter. As a corollary we also compute low dimensional homotopy groups of the moduli space of α-stable representations of the quiver with fixed dimension vector, and apply the theory to the space of non-degenerate polygons in three-dimensional Euclidean space.

scholarly journals Classifying spaces for commutativity of low-dimensional Lie groups

2019 ◽  
Vol 169 (3) ◽  
pp. 433-478 ◽  
Author(s):  
OMAR ANTOLÍN–CAMARENA ◽  
SIMON PHILIPP GRITSCHACHER ◽  
BERNARDO VILLARREAL
Keyword(s):  
Lie Groups ◽  
Homotopy Type ◽  
Steenrod Algebra ◽  
Homotopy Groups ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Cohomology Rings ◽  
Homotopy Fiber ◽  
Low Dimensional

AbstractFor each of the groups G = O(2), SU(2), U(2), we compute the integral and $\mathbb{F}_2$-cohomology rings of BcomG (the classifying space for commutativity of G), the action of the Steenrod algebra on the mod 2 cohomology, the homotopy type of EcomG (the homotopy fiber of the inclusion BcomG → BG), and some low-dimensional homotopy groups of BcomG.

Thermoelectric Properties of PbSr(Se,Te)-Based Low Dimensional Structures

2000 ◽  
Vol 626 ◽  
Author(s):  
Harald Beyer ◽  
Joachim Nurnus ◽  
Harald Böttner ◽  
Armin Lambrecht ◽  
Lothar Schmitt ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermoelectric Properties ◽  
Power Factor ◽  
Evaluation Method ◽  
Interband Transition ◽  
Multiple Quantum Well ◽  
Calculated Data ◽  
Multiple Quantum ◽  
Ir Transmission ◽  
Low Dimensional

ABSTRACTThermoelectric properties of low dimensional structures based on PbTe/PbSrTe-multiple quantum-well (MQW)-structures with regard to the structural dimensions, doping profiles and levels are presented. Interband transition energies and barrier band-gap are determined from IR-transmission spectra and compared with Kronig-Penney calculations. The influence of the data evaluation method to obtain the 2D power factor will be discussed. The thermoelectrical data of our layers show a more modest enhancement in the power factor σS2 compared with former publications and are in good agreement with calculated data from Broido et al. [5]. The maximum allowed doping level for modulation doped MQW structures is determined. Thermal conductivity measurements show that a ZT enhancement can be achieved by reducing the thermal conductivity due to interface scattering. Additionally promising lead chalcogenide based superlattices for an increased 3D figure of merit are presented.

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