Autoencoders Covering Space as a Life-Long Classifier

2019 ◽  
pp. 271-281
Author(s):  
Rudolf Szadkowski ◽  
Jan Drchal ◽  
Jan Faigl
Keyword(s):  
Covering Space

Minimal Plat Representations of Prime Knots and Links are not Unique

1976 ◽  
Vol 28 (1) ◽  
pp. 161-167 ◽  
Author(s):  
José M. Montesinos
Keyword(s):  
Infinite Family ◽  
Equivalence Classes ◽  
Covering Space ◽  
Heegaard Splittings ◽  
Cyclic Covering ◽  
Knots And Links

Letdenote the 2-fold cyclic covering space branched over a linkLin S3. We wish to describe an infinite family of prime knots and links in which each memberLexhibits two minimal 6-plat representations, where the associated Heegaard splittings ofare minimal and inequivalent. Thus each knot or link of that family admits at least two equivalence classes of 6-plat representations which are minimal.

A quadratic parabolic group

1975 ◽  
Vol 77 (2) ◽  
pp. 281-288 ◽  
Author(s):  
Robert Riley
Keyword(s):  
Normal Form ◽  
Half Space ◽  
Transformation Group ◽  
Universal Covering ◽  
Covering Space ◽  
Fundamental Domains ◽  
Universal Covering Space ◽  
Other Information ◽  
Figure Eight Knot

When k is a 2-bridge knot with group πK, there are parabolic representations (p-reps) θ: πK → PSL(): = PSL(2, ). The most obvious problem that this suggests is the determination of a presentation for an image group πKθ. We shall settle the easiest outstanding case in section 2 below, viz. k the figure-eight knot 41, which has the 2-bridge normal form (5, 3). We shall prove that the (two equivalent) p-reps θ for this knot are isomorphisms of πK on πKθ. Furthermore, the universal covering space of S3\k can be realized as Poincaré's upper half space 3, and πKθ is a group of hyperbolic isometries of 3 which is also the deck transformation group of the covering 3 → S3\k. The group πKθ is a subgroup of two closely related groups that we study in section 3. We shall give fundamental domains, presentations, and other information for all these groups.

FRACTIONAL SPIN ON THE SPHERE AND THE BREAKING OF ROTATIONAL INVARIANCE

1991 ◽  
Vol 06 (06) ◽  
pp. 521-526
Author(s):  
G. BIMONTE ◽  
G. SPARANO
Keyword(s):  
Rotational Invariance ◽  
Covering Space ◽  
Subsequent Paper ◽  
Half Integer ◽  
Fractional Spin ◽  
Classical Symmetries ◽  
Apparent Disagreement

Topological considerations, in apparent disagreement with operatorial ones, seem to suggest that only integer and half-integer spins are possible on a sphere. In this letter we show that fractional spin is indeed possible on a sphere, but only by breaking the rotational invariance. As we will show in a subsequent paper, this is an example of the fact that the quantizations individuated by the covering space are those that preserve the continuous classical symmetries.

scholarly journals Limits of covering spaces and residual properties of groups

1994 ◽  
Vol 36 (3) ◽  
pp. 277-282
Author(s):  
Jon Michael Corson
Keyword(s):  
Covering Space ◽  
Covering Spaces ◽  
Residually Finite ◽  
Residual Properties ◽  
Space Approach

The purpose of this paper is to point out a flaw in H. B. Griffiths' covering space approach to residual properties of groups [3]. One is led to this paper from Lyndon and Schupp's book [4, pp. 114, 141] where it is cited for covering space methods and a proof that F-groups are residually finite. However the main result of [3] is false.

Rigidities of asymptotically Euclidean manifolds

1999 ◽  
Vol 60 (3) ◽  
pp. 521-528 ◽  
Author(s):  
Seong-Hun Paeng
Keyword(s):  
Riemannian Manifold ◽  
Euclidean Space ◽  
Fundamental Group ◽  
Compact Riemannian Manifold ◽  
Universal Covering ◽  
Covering Space ◽  
Universal Covering Space

Let M be an n-dimensional compact Riemannian manifold. We study the fundamental group of M when the universal covering space of M, M is close to some Euclidean space ℝs asymptotically.

scholarly journals A presentation for a group of automorphisms of a simplicial complex

1988 ◽  
Vol 30 (3) ◽  
pp. 331-337 ◽  
Author(s):  
M. A. Armstrong
Keyword(s):  
Simplicial Complex ◽  
Elementary Proof ◽  
Universal Covering ◽  
Covering Space ◽  
Covering Spaces ◽  
Group Of Automorphisms ◽  
Generators And Relations ◽  
Universal Covering Space ◽  
Simply Connected ◽  
Special Case

The Bass–Serre theorem supplies generators and relations for a group of automorphisms of a tree. Recently K. S. Brown [2] has extended the result to produce a presentation for a group of automorphisms of a simply connected complex, the extra ingredient being relations which come from the 2-cells of the complex. Suppose G is the group, K the complex and L the 1-skeleton of K. Then an extension of π1(L) by G acts on the universal covering space of L (which is of course a tree) and Brown's technique is to apply the work of Bass and Serre to this action. Our aim is to give a direct elementary proof of Brown's theorem which makes no use of covering spaces, deals with the Bass–Serre theorem as a special case and clarifies the roles played by the various generators and relations.

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