Publications
Preprints
These have been submitted to various journals but are still under review and may be subject to change/improvement/disimprovement/retraction/etc...
Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints. With Fatemeh Mohammadi, Anthony Nixon and Shin-ichi Tanigawa https://arxiv.org/abs/2305.18990
Rigidity of Symmetric Simplicial Complexes and the Lower Bound Theorem. With Bill Jackson and Shin-ichi Tanigawa https://arxiv.org/abs/2304.04693
Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs. With Bernd Schulze. https://arxiv.org/abs/2006.10519
Journal papers
The links are to the journal versions so you may hit a paywall. Almost all of my papers are also available from the arXiv. In some cases the arXiv version is slightly different from the journal version.
James Cruickshank, Bill Jackson, Shin-ichi Tanigawa. Global rigidity of triangulated manifolds. Advances in Mathematics, Volume 458, Part A, 2024, 109953. link
Chen, B.G., Cruickshank, J., Kitson, D. (2024). Block-and-Hole Graphs: Constructibility and (3,0)-Sparsity. Mathematical Proceedings of the Royal Irish Academy 124(2), 53-69. link
Cruickshank, James; Mohammadi, Fatemeh; Motwani, Harshit J.; Nixon, Anthony; Tanigawa, Shin-ichi. Global Rigidity of Line Constrained Frameworks. SIAM Journal on Discrete Mathematics (2024). link
Cruickshank, J., Kastis, E., Kitson, D. et al. Braced Triangulations and Rigidity. Discrete Comput Geom 71, 1238–1275 (2024). link
Cruickshank, James; Jackson, Bill; Tanigawa, Shin-ichi . Vertex splitting, coincident realisations, and global rigidity of braced triangulations. Discrete Comput. Geom. 69 (2023), no. 1, 192--208. link
Cruickshank, James; Kitson, Derek; Power, Stephen C.; Shakir, Qays . Topological inductive constructions for tight surface graphs. Graphs Combin. 38 (2022), no. 6, Paper No. 169, 31 pp. link
Cruickshank, James ; Guler, Hakan ; Jackson, Bill ; Nixon, Anthony . Rigidity of linearly constrained frameworks. Int. Math. Res. Not. IMRN 2020, no. 12, 3824--3840. link
Cruickshank, J. ; Gutiérrez Frez, L. ; Szechtman, F. Weil representations via abstract data and Heisenberg groups: a comparison. J. Algebra 547 (2020), 129--161. link
Cruickshank, J. ; Kitson, D. ; Power, S. C. The rigidity of a partially triangulated torus. Proc. Lond. Math. Soc. (3) 118 (2019), no. 5, 1277--1304. link
Cruickshank, J. ; Szechtman, F. Unitary groups and ramified extensions. Comm. Algebra 47 (2019), no. 1, 101--113. link
Cruickshank, J. ; Szechtman, F. Generators and relations for the unitary group of a skew hermitian form over a local ring. Linear Algebra Appl. 552 (2018), 1--28. link
Cruickshank, James ; Quinlan, Rachel ; Szechtman, Fernando . Hermitian and skew hermitian forms over local rings. Linear Algebra Appl. 551 (2018), 147--161. link
Cruickshank, James ; Loane, John ; Ryan, Raymond A. Positive polynomials on Riesz spaces. Positivity 21 (2017), no. 3, 885--895. link
Cruickshank, James ; Kitson, Derek ; Power, Stephen C. The generic rigidity of triangulated spheres with blocks and holes. J. Combin. Theory Ser. B 122 (2017), 550--577. link
Cruickshank, James . On spaces of infinitesimal motions and three dimensional Henneberg extensions. Discrete Comput. Geom. 51 (2014), no. 3, 702--721. link
Cruickshank, James ; McLaughlin, Jonathan . The smooth structure of the moduli space of a weighted series-parallel graph. Topology Appl. 164 (2014), 242--247. link
Cruickshank, J. ; Herman, A. ; Quinlan, R. ; Szechtman, F. Unitary groups over local rings. J. Algebra Appl. 13 (2014), no. 2, 1350093, 23 pp. link
Cruickshank, James ; McLaughlin, Jonathan . Series parallel linkages. Publ. Mat. 55 (2011), no. 2, 359--378. link
Newell, J; Higgins, D; Madden, N; Cruickshank, J; Einbeck, J; McMillan, K; McDonald, R (2007) Software for calculating blood lactate endurance markers. Journal Of Sports Sciences, 25 :1403-1409. link
Cruickshank, James ; Kelly, Séamus . Rearrangement inequalities and the alternahedron. Discrete Comput. Geom. 35 (2006), no. 2, 241--254. link
Cruickshank, James. Twisted homotopy theory and the geometric equivariant 1-stem. Topology Appl. 129 (2003), no. 3, 251--271. link
Conference publications
James Cruickshank and Qays Shakir (2020) Contacts of Circular Arcs Representations of Tight Surface Graphs . In: Auber, David and Valtr, Pavel eds. Graph Drawing and Network Visualization Vancouver, , pp.529-531
Marshall, C;O'Riordan, C;Cruickshank, J (2018) Targeting Influential Nodes for Recovery in Bootstrap Percolation on Hyperbolic Networks NETWORK INTELLIGENCE MEETS USER CENTERED SOCIAL MEDIA NETWORKS , pp.3-16
Marshall, C;Cruickshank, J;O'Riordan, C (2018) Identifying Influential Nodes to Inhibit Bootstrap Percolation on Hyperbolic Networks 2018 IEEE/ACM INTERNATIONAL CONFERENCE ON ADVANCES IN SOCIAL NETWORKS ANALYSIS AND MINING (ASONAM) , pp.1266-1273
Marshall, C;Cruickshank, J;O'Riordan, C (2018) Identifying a Game-Theoretic Transition on Hyperbolic Networks, IADIS International Conference Big Data Analytics, Data Mining and Computational Intelligence, pp 97-104
Marshall, C;Cruickshank, J;O'Riordan, C (2014) Investigating Properties of Random Geometric Graph, IADIS International Conference on Intelligent Systems & Agents, pp 263-264
Thesis
Twisted cobordism and its relationship to equivariant homotopy theory. Thesis (Ph.D.)–University of Alberta (Canada). ProQuest LLC, Ann Arbor, MI, 1999. 87 pp. ISBN: 978-0612-46823-8