Publications

Preprints

These have been submitted to various journals but are still under review and may be subject to change/improvement/disimprovement/retraction/etc...

1. 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 

2. Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs. With Bernd Schulze. https://arxiv.org/abs/2006.10519 

Journal Articles

The links are to the journal versions so you may hit a paywall. Most of my papers are also available from the arXiv.  In some cases the arXiv version is slightly different from the journal version. 

1. James Cruickshank, Bill Jackson, Shin-ichi Tanigawa. Rigidity of Symmetric Simplicial Complexes and the Lower Bound Theorem. To appear in Forum of Mathematics, Sigma. preprint version: https://arxiv.org/abs/2304.04693 

2. James Cruickshank, Bill Jackson, Shin-ichi Tanigawa. Global rigidity of triangulated manifolds. Advances in Mathematics, Volume 458, Part A, 2024, 109953. link

3. 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

4. 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

5. Cruickshank, J., Kastis, E., Kitson, D. et al. Braced Triangulations and Rigidity. Discrete Comput Geom 71, 1238–1275 (2024). link

6. 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

7. 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

8. Cruickshank, James ;  Guler, Hakan ;  Jackson, Bill ;  Nixon, Anthony . Rigidity of linearly constrained frameworks. Int. Math. Res. Not. IMRN  2020,  no. 12, 3824--3840. link

9. Cruickshank, J. ;  Gutiérrez Frez, L. ;  Szechtman, F.  Weil representations via abstract data and Heisenberg groups: a comparison. J. Algebra 547 (2020), 129--161. link

10. 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

11. Cruickshank, J. ;  Szechtman, F.  Unitary groups and ramified extensions. Comm. Algebra  47  (2019),  no. 1, 101--113. link 

12. 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

13. Cruickshank, James ;  Quinlan, Rachel ;  Szechtman, Fernando . Hermitian and skew hermitian forms over local rings. Linear Algebra Appl. 551 (2018), 147--161. link

14. Cruickshank, James ;  Loane, John ;  Ryan, Raymond A.  Positive polynomials on Riesz spaces. Positivity  21  (2017),  no. 3, 885--895. link

15. 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

16. Cruickshank, James . On spaces of infinitesimal motions and three dimensional Henneberg extensions. Discrete Comput. Geom.  51  (2014),  no. 3, 702--721. link

17. Cruickshank, James ;  McLaughlin, Jonathan . The smooth structure of the moduli space of a weighted series-parallel graph. Topology Appl.  164  (2014), 242--247. link

18.  Cruickshank, J. ;  Herman, A. ;  Quinlan, R. ;  Szechtman, F.  Unitary groups over local rings. J. Algebra Appl.  13  (2014),  no. 2, 1350093, 23 pp. link

19. Cruickshank, James ;  McLaughlin, Jonathan . Series parallel linkages. Publ. Mat.  55  (2011),  no. 2, 359--378. link

20. 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

21. Cruickshank, James ;  Kelly, Séamus . Rearrangement inequalities and the alternahedron. Discrete Comput. Geom.  35  (2006),  no. 2, 241--254. link

22. Cruickshank, James. Twisted homotopy theory and the geometric equivariant 1-stem. Topology Appl.  129  (2003),  no. 3, 251--271. link

Conference Publications

1. 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 

2. 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 

3. 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 

4. 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

5. 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