ORCID Profile
0000-0002-8167-6226
Current Organisations
Nanyang Technological University
,
University of Sydney
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Publisher: Mathematical Sciences Publishers
Date: 25-11-2004
Publisher: Cambridge University Press (CUP)
Date: 10-1993
DOI: 10.1017/S1446788700032006
Abstract: There are 11 closed 4-manifolds which admit geometries of compact type ( S 4 , CP 2 or S 2 × S 2 ) and two other closely related bundle spaces ( S 2 × S 2 and the total space of the nontrivial RP 2 -bundle over S 2 ). We show that the homotopy type of such a manifold is determined up to an ambiguity of order at most 4 by its quadratic 2-type, and this in turn is (in most cases) determined by the Euler characteristic, fundamental group and Stiefel-Whitney classes. In (at least) seven of the 13 cases, a PL 4-manifold with the same invariants as a geometric manifold or bundle space must be homeomorphic to it.
Publisher: World Scientific Pub Co Pte Lt
Date: 12-2020
DOI: 10.1142/S0218216520500947
Abstract: We consider embeddings of 3-manifolds [Formula: see text] in [Formula: see text] such that the two complementary regions [Formula: see text] and [Formula: see text] each have nilpotent fundamental group. If [Formula: see text] is odd then these groups are abelian and [Formula: see text]. In general [Formula: see text] and [Formula: see text] have 3-generator presentations, and [Formula: see text]. We give two ex les illustrating our results.
Publisher: Mathematical Sciences Publishers
Date: 24-02-2012
Publisher: WORLD SCIENTIFIC
Date: 2007
Publisher: Springer Science and Business Media LLC
Date: 09-10-2007
Publisher: Elsevier BV
Date: 03-2023
Publisher: Elsevier BV
Date: 09-2022
Publisher: Cambridge University Press (CUP)
Date: 08-1987
DOI: 10.1017/S1446788700028913
Abstract: We compute the kernel of cup product of 1-dimensional cohomology classes for a group G acting trivially on Z or F 2 , by means of the naturality of cup product and the 5-term exact sequence of low degree of a suitable LHS spectral sequence. We determine thereby when cup product is injective, and when it is null.
Publisher: WORLD SCIENTIFIC
Date: 15-05-2012
DOI: 10.1142/8493
Publisher: World Scientific Pub Co Pte Lt
Date: 2020
DOI: 10.1142/S0218216519500949
Abstract: We extend the classical definition of width to higher dimensional, smooth codimension two knots and show in each dimension there are knots of arbitrarily large width.
Publisher: Walter de Gruyter GmbH
Date: 24-02-2022
Abstract: We show that if a nilpotent group 𝐺 has a balanced presentation and Hirsch length h ( G ) 3 h(G) , then β 1 ( G Q ) = 2 \\beta_{1}(G \\mathbb{Q})=2 . There is one such group which is torsion-free and of Hirsch length h = 4 h=4 , and none with h = 5 h=5 . We also construct a torsion-free nilpotent group 𝐺 with h ( G ) = 6 h(G)=6 and β 2 ( G F ) = β 1 ( G F ) \\beta_{2}(G F)=\\beta_{1}(G F) for all fields 𝐹.
Publisher: Walter de Gruyter GmbH
Date: 03-08-2023
Abstract: We show that torsion-free elementary amenable groups of Hirsch length at most 3 are solvable, of derived length at most 3. This class includes all solvable groups of cohomological dimension 3. We show also that groups in the latter subclass are either polycyclic, semidirect products BS ( 1 , n ) ⋊ Z \\mathrm{BS}(1,n)\\rtimes\\mathbb{Z} , or properly ascending HNN extensions with base Z 2 \\mathbb{Z}^{2} or π 1 ( Kb ) \\pi_{1}(\\mathrm{Kb}) .
Publisher: Elsevier BV
Date: 09-2005
Publisher: Springer Science and Business Media LLC
Date: 12-1981
DOI: 10.1007/BF01214764
Publisher: Springer Science and Business Media LLC
Date: 09-1985
DOI: 10.1007/BF01215136
Publisher: World Scientific Pub Co Pte Lt
Date: 2020
DOI: 10.1142/S0218216520500017
Abstract: We consider embeddings of 3-manifolds in [Formula: see text] such that each of the two complementary regions has an abelian fundamental group. In particular, we show that an homology handle [Formula: see text] has such an embedding if and only if [Formula: see text] is perfect, and that the embedding is then essentially unique.
Publisher: MDPI AG
Date: 24-11-2020
DOI: 10.3390/APP10238350
Abstract: With the development of Industry 4.0, additive manufacturing will be widely used to produce customized components. However, it is rather time-consuming and expensive to produce components with sound structure and good mechanical properties using additive manufacturing by a trial-and-error approach. To obtain optimal process conditions, numerous experiments are needed to optimize the process variables within given machines and processes. Digital twins (DT) are defined as a digital representation of a production system or service or just an active unique product characterized by certain properties or conditions. They are the potential solution to assist in overcoming many issues in additive manufacturing, in order to improve part quality and shorten the time to qualify products. The DT system could be very helpful to understand, analyze and improve the product, service system or production. However, the development of genuine DT is still impeded due to lots of factors, such as the lack of a thorough understanding of the DT concept, framework, and development methods. Moreover, the linkage between existing brownfield systems and their data are under development. This paper aims to summarize the current status and issues in DT for additive manufacturing, in order to provide more references for subsequent research on DT systems.
Publisher: American Mathematical Society
Date: 2013
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 12-1986
DOI: 10.1007/BF02621906
Publisher: Cambridge University Press (CUP)
Date: 12-2004
DOI: 10.1017/S1446788700014476
Abstract: We give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply to PD n -groups which are virtually poly- Z or have a Kropholler decomposition into parts of generalized Seifert type, for all n .
Publisher: Cambridge University Press (CUP)
Date: 04-1984
DOI: 10.1017/S0004972700021420
Abstract: If A is a Dedekind domain and f generates a prime ideal of A [ X ] which is not maximal, then the domain A [ X ]/( f ) is Dedekind if and only if f is not contained in the square of any maximal ideal of A [ X ]. This criterion is used find the ring of integers of a cyclotomic field, and to determine when a plane curve is normal.
Publisher: Wiley
Date: 29-07-2010
Publisher: Elsevier BV
Date: 10-2022
Publisher: World Scientific Pub Co Pte Lt
Date: 10-2017
DOI: 10.1142/S0218216517500663
Abstract: If [Formula: see text] is an orientable, strongly minimal [Formula: see text]-complex and [Formula: see text] has one end, then it has no nontrivial locally finite normal subgroup. Hence, if [Formula: see text] is a 2-knot group, then (a) if [Formula: see text] is virtually solvable, then either [Formula: see text] has two ends or [Formula: see text], with presentation [Formula: see text], or [Formula: see text] is torsion-free and polycyclic of Hirsch length 4 (b) either [Formula: see text] has two ends, or [Formula: see text] has one end and the center [Formula: see text] is torsion-free, or [Formula: see text] has infinitely many ends and [Formula: see text] is finite, and (c) the Hirsch–Plotkin radical [Formula: see text] is nilpotent.
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Jonathan Hillman.