THE THIRD HOMOTOPY GROUP OF SOME HIGHER DIMENSIONAL KNOTS

1975 ◽  
pp. 35-46
Author(s):  
S. J . Lomonaco
Keyword(s):  
Homotopy Group ◽  
The Third ◽  
Higher Dimensional

scholarly journals The third way to 3D gravity

2015 ◽  
Vol 24 (12) ◽  
pp. 1544015 ◽  
Author(s):  
Eric Bergshoeff ◽  
Wout Merbis ◽  
Alasdair J. Routh ◽  
Paul K. Townsend
Keyword(s):  
Equations Of Motion ◽  
Massive Gravity ◽  
De Sitter ◽  
Gravitational Field Equation ◽  
Third Way ◽  
Metric Tensor ◽  
The Third ◽  
Higher Dimensional ◽  
Conservation Condition ◽  
3D Gravity

Consistency of Einstein’s gravitational field equation [Formula: see text] imposes a “conservation condition” on the [Formula: see text]-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a “nongeometrical” action: one not constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D “minimal massive gravity” model, which resolves the “bulk versus boundary” unitarity problem of topologically massive gravity with Anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher dimensional theories.

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

Mixing sets and relative entropies for higher-dimensional Markov shifts

1993 ◽  
Vol 13 (4) ◽  
pp. 705-735 ◽  
Author(s):  
Bruce Kitchens ◽  
Klaus Schmidt
Keyword(s):  
Higher Order ◽  
The Third ◽  
Markov Shifts ◽  
Higher Dimensional ◽  
Probability Spaces ◽  
Mixing Behaviour

AbstractWe consider certain measurable isomorphism invariants for measure-preserving ℤd-actions on probability spaces, compute them for a class of d-dimensional Markov shifts, and use them to prove that some of these examples are non-isomorphic. The invariants under discussion are of three kinds: the first is associated with the higher-order mixing behaviour of the ℤd-action, and is related—in this class of examples—to an an arithmetical result by David Masser, the second arises from certain relative entropies associated with the ℤd-action, and the third is a collection of canonical invariant σ-algebras. The results of this paper are generalizations of earlier results by Kitchens and Schmidt, and we include a proof of David Masser's unpublished theorem.

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

Ehrenfest scheme of higher dimensional AdS black holes in the third-order Lovelock–Born–Infeld gravity

2015 ◽  
Vol 12 (10) ◽  
pp. 1550115 ◽  
Author(s):  
A. Belhaj ◽  
M. Chabab ◽  
H. EL Moumni ◽  
K. Masmar ◽  
M. B. Sedra
Keyword(s):  
Black Holes ◽  
Critical Points ◽  
Space Dimension ◽  
Second Phase ◽  
Third Order ◽  
The Third ◽  
Ads Black Holes ◽  
Higher Dimensional ◽  
Number Formula ◽  
Thermodynamic Pressure

Interpreting the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the investigation of P–V critical behaviors of (1 + n)-dimensional AdS black holes in Lovelock–Born–Infeld gravity. In particular, we derive an explicit expression of the universal number [Formula: see text] in terms of the space dimension n. Then, we examine the phase transitions at the critical points of such black holes for 6 ≤ n < 11 as required by the physical condition of the thermodynamical quantities including criticality behaviors. More precisely, the Ehrenfest equations have been checked and they reveal that the black hole system undergoes a second phase transition at the critical points.

scholarly journals Drinfeld–Manin solutions of the Yang–Baxter equation coming from cube complexes

2021 ◽  
pp. 1-14
Author(s):  
Alina Vdovina
Keyword(s):  
Geometric Interpretation ◽  
Reidemeister Move ◽  
Baxter Equation ◽  
The Third ◽  
Reidemeister Moves ◽  
Explicit Constructions ◽  
Higher Dimensional ◽  
Dimensional Cube ◽  
Cube Complexes ◽  
By Products

The most common geometric interpretation of the Yang–Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are higher-dimensional cube complexes solving the [Formula: see text]-state Yang–Baxter equation for arbitrarily large [Formula: see text]. More precisely, we introduce explicit constructions of cube complexes covered by products of [Formula: see text] trees and show that these cube complexes lead to new solutions of the Yang–Baxter equations.

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 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
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