scholarly journals On the third homotopy group of Orr’s space

2018 ◽  
Vol 18 (1) ◽  
pp. 569-582
Author(s):  
Emmanuel Dror Farjoun ◽  
Roman Mikhailov
Keyword(s):  
Homotopy Group ◽  
The Third

scholarly journals On the non-abelian tensor square of all groups of order dividing p5

2020 ◽  
pp. 2150107
Author(s):  
Taleea Jalaeeyan Ghorbanzadeh ◽  
Mohsen Parvizi ◽  
Peyman Niroomand
Keyword(s):  
Homotopy Group ◽  
The Third ◽  
Tensor Square ◽  
Exterior Square

In this paper, we consider all groups of order dividing [Formula: see text]. We obtain the explicit structure of the non-abelian tensor square, non-abelian exterior square, tensor center, exterior center, the third homotopy group of suspension of an Eilenberg–MacLane space [Formula: see text] and [Formula: see text] of such groups.

scholarly journals On the size of the third homotopy group of the suspension of an Eilenberg--MacLane space

2014 ◽  
Vol 38 ◽  
pp. 664-671 ◽  
Author(s):  
Peyman NIROOMAND ◽  
Francesco G. RUSSO
Keyword(s):  
Homotopy Group ◽  
The Third

scholarly journals The third homotopy group as a $$\pi _1$$ π 1 -module

2015 ◽  
Vol 26 (1-2) ◽  
pp. 165-189
Author(s):  
Hans-Joachim Baues ◽  
Beatrice Bleile
Keyword(s):  
Homotopy Group ◽  
The Third

The non-abelian tensor square of p-groups of order p4

2018 ◽  
Vol 11 (06) ◽  
pp. 1850084
Author(s):  
Taleea Jalaeeyan Ghorbanzadeh ◽  
Mohsen Parvizi ◽  
Peyman Niroomand
Keyword(s):  
Homotopy Group ◽  
The Third ◽  
Tensor Square ◽  
Exterior Square

In this paper, in the class of [Formula: see text]-groups of order [Formula: see text], we obtain the non-abelian exterior square, the exterior center, the non-abelian tensor square, the tensor center and the third homotopy group of suspension of an Eilenberg–MacLane space [Formula: see text] of such groups.

scholarly journals INTERSECTION OF SUBGROUPS IN FREE GROUPS AND HOMOTOPY GROUPS

2008 ◽  
Vol 18 (05) ◽  
pp. 803-823 ◽  
Author(s):  
HANS-JOACHIM BAUES ◽  
ROMAN MIKHAILOV
Keyword(s):  
Abelian Group ◽  
Free Group ◽  
Homotopy Group ◽  
Homotopy Groups ◽  
Natural Homomorphism ◽  
Two Dimensional ◽  
The Third ◽  
Cw Complex ◽  
Intersection Of Subgroups ◽  
The Right

We show that the intersection of three subgroups in a free group is related to the computation of the third homotopy group π3. This generalizes a result of Gutierrez–Ratcliffe who relate the intersection of two subgroups with the computation of π2. Let K be a two-dimensional CW-complex with subcomplexes K1, K2, K3 such that K = K1 ∪ K2 ∪ K3 and K1 ∩ K2 ∩ K3 is the 1-skeleton K1 of K. We construct a natural homomorphism of π1(K)-modules [Formula: see text] where Ri = ker {π1(K1) → π1(Ki)}, i = 1,2,3 and the action of π1(K) = F/R1R2R3 on the right-hand abelian group is defined via conjugation in F. In certain cases, the defined map is an isomorphism. Finally, we discuss certain applications of the above map to group homology.

scholarly journals On Pierce-like idempotents and Hopf invariants

2003 ◽  
Vol 2003 (62) ◽  
pp. 3903-3920
Author(s):  
Giora Dula ◽  
Peter Hilton
Keyword(s):  
Homotopy Group ◽  
Hopf Invariant ◽  
The Third ◽  
Direct Sum ◽  
Direct Sum Decomposition ◽  
Matrix Calculus ◽  
Hopf Invariants

Given a setKwith cardinality‖K‖ =n, a wedge decomposition of a spaceYindexed byK, and a cogroupA, the homotopy groupG=[A,Y]is shown, by using Pierce-like idempotents, to have a direct sum decomposition indexed byP(K)−{ϕ}which is strictly functorial ifGis abelian. Given a classρ:X→Y, there is a Hopf invariantHIρon[A,Y]which extends Hopf's definition whenρis a comultiplication. ThenHI=HIρis a functorial sum ofHILoverL⊂K,‖L‖ ≥2. EachHILis a functorial composition of four functors, the first depending only onAn+1, the second only ond, the third only onρ, and the fourth only onYn. There is a connection here with Selick and Walker's work, and with the Hilton matrix calculus, as described by Bokor (1991).

Progress report on 21-cm observations at low latitude between longitudes (l 11) 0° and 66°

1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane
Keyword(s):  
Preliminary Report ◽  
Progress Report ◽  
Galactic Centre ◽  
Low Latitude ◽  
The Third ◽  
Introductory Lecture ◽  
Centre Region

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

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