The generalized radiation gauge for a simply connected space-time

AbstractWe answer the following question posed by Lechuga: given a simply connected spaceXwith bothH*(X; ℚ) and π*(X) ⊗ ℚ being finite dimensional, what is the computational complexity of an algorithm computing the cup length and the rational Lusternik—Schnirelmann category ofX?Basically, by a reduction from the decision problem of whether a given graph isk-colourable fork≥ 3, we show that even stricter versions of the problems above are NP-hard.

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The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500021004 ◽

1992 ◽

Vol 122 (1-2) ◽

pp. 127-135 ◽

Cited By ~ 1

Author(s):

John W. Rutter

Keyword(s):

Group Extension ◽

Equivalence Classes ◽

Homotopy Groups ◽

Geometric Proof ◽

Homotopy Equivalence ◽

Connected Space ◽

Abelian Kernel ◽

Simply Connected ◽

Extension Sequence ◽

Connected Spaces

SynopsisWe give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.

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Whitney-sums (fibre-joins) in over space theory and obstruction theory for cohomology with local coefficients

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500020709 ◽

1990 ◽

Vol 115 (3-4) ◽

pp. 359-365 ◽

Cited By ~ 1

Author(s):

John W. Rutter

Keyword(s):

Obstruction Theory ◽

Space Theory ◽

Connected Space ◽

Local Coefficient ◽

General Properties ◽

Local Coefficients ◽

Simply Connected ◽

Cohomology With Local Coefficients ◽

Cohomology Sequence

SynopsisThe generalised Whitney sum (fibre-join) and the h-fibre-join can be defined in topM, the category of spaces over M. We note here some general properties of these constructions, and, as a specific example, we consider the relation between them and the extensions to the topM category of the top h-fibre-sequences F∗ΩB→E ∪ CF→B determined by top fibrations F→E→B. As an application we obtain the truncated local coefficient cohomology sequence for a top fibration which is topM principal fibration: this situation applies, for example, to the various stages of the Postnikov decomposition of a non-simply connected space X, and in this case we have M = K1(π1(X)).

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The free topological group on a simply connected space

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1976-0424993-8 ◽

1976 ◽

Vol 55 (1) ◽

pp. 155-155 ◽

Cited By ~ 3

Author(s):

J. P. L. Hardy ◽

Sidney A. Morris

Keyword(s):

Topological Group ◽

Connected Space ◽

Free Topological Group ◽

Simply Connected

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Harmonic morphisms and conformal foliations by geodesics of three-dimensional space forms

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700033358 ◽

1991 ◽

Vol 51 (1) ◽

pp. 118-153 ◽

Cited By ~ 13

Author(s):

Paul Baird ◽

John C. Wood

Keyword(s):

Space Form ◽

Holomorphic Mapping ◽

Dimensional Space ◽

Three Dimensional ◽

Complete Classification ◽

Harmonic Morphisms ◽

Connected Space ◽

Space Forms ◽

Simply Connected ◽

Three Dimensional Space

AbstractA complete classification is given of harmonic morphisms to a surface and conformal foliations by geodesics, with or without isolated singularities, of a simply-connected space form. The method is to associate to any such a holomorphic map from a Riemann surface into the space of geodesics of the space form. Properties such as nonintersecting fibres (or leaves) are translated into conditions on the holomorphic mapping which show it must have a simple form corresponding to a standard example.

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