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. Block-and-hole graphs: Constructibility and (3,0)-sparsity.  With Bryan Gin-ge Chen and Derek Kitson https://arxiv.org/abs/2309.06804 

2. 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 

3. Rigidity of Symmetric Simplicial Complexes and the Lower Bound Theorem. With Bill Jackson and Shin-ichi Tanigawa https://arxiv.org/abs/2304.04693 

4. Global Rigidity of Triangulated Manifolds. With Bill Jackson and Shin-ichi Tanigawa https://arxiv.org/abs/2204.02503

5. 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. 

1. 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

2. Cruickshank, J., Kastis, E., Kitson, D. et al. Braced Triangulations and Rigidity. Discrete Comput Geom (2023). link

3. 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

4. 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

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

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

7. 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

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

9. 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

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

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

12. 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

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

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

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

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

17. 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

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

19. 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