Grant Cairns

1.9k total citations · 1 hit paper
60 papers, 1.1k citations indexed

About

Grant Cairns is a scholar working on Geometry and Topology, Mathematical Physics and Algebra and Number Theory. According to data from OpenAlex, Grant Cairns has authored 60 papers receiving a total of 1.1k indexed citations (citations by other indexed papers that have themselves been cited), including 32 papers in Geometry and Topology, 22 papers in Mathematical Physics and 16 papers in Algebra and Number Theory. Recurrent topics in Grant Cairns's work include Mathematics and Applications (11 papers), Mathematical Dynamics and Fractals (11 papers) and Advanced Topics in Algebra (10 papers). Grant Cairns is often cited by papers focused on Mathematics and Applications (11 papers), Mathematical Dynamics and Fractals (11 papers) and Advanced Topics in Algebra (10 papers). Grant Cairns collaborates with scholars based in Australia, Canada and United States. Grant Cairns's co-authors include James K. Brooks, P. J. Stacey, John Banks, Gary Davis, Daniel M. Elton, Yuri Nikolayevsky, John Bamberg, R. W. Sharpe, Étienne Ghys and Tamás Lengyel and has published in prestigious journals such as Transactions of the American Mathematical Society, American Mathematical Monthly and Bulletin of the London Mathematical Society.

In The Last Decade

Grant Cairns

49 papers receiving 980 citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

On Devaney's Definition of Chaos

1992 472 citations Grant Cairns et al. American Mathematical Monthly profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Grant Cairns Australia	13	637	448	408	197	166	60	1.1k
Serge Tabachnikov United States	21	746 1.2×	643 1.4×	908 2.2×	159 0.8×	286 1.7×	129	1.5k
Hillel Fürstenberg Israel	14	1.1k 1.7×	289 0.6×	744 1.8×	451 2.3×	163 1.0×	29	1.8k
Marian Mrożek Poland	23	819 1.3×	594 1.3×	357 0.9×	748 3.8×	54 0.3×	76	1.6k
Caroline Series United Kingdom	18	869 1.4×	235 0.5×	701 1.7×	206 1.0×	219 1.3×	48	1.2k
Rick Miranda United States	18	430 0.7×	168 0.4×	851 2.1×	264 1.3×	160 1.0×	74	1.2k
Welington de Melo Brazil	11	1.4k 2.2×	1.1k 2.4×	914 2.2×	318 1.6×	322 1.9×	18	2.3k
Gerald A. Edgar United States	18	818 1.3×	180 0.4×	289 0.7×	305 1.5×	347 2.1×	51	1.4k
Dmitri Burago United States	12	582 0.9×	178 0.4×	969 2.4×	401 2.0×	942 5.7×	32	1.7k
Анатолий Тимофеевич Фоменко	12	167 0.3×	321 0.7×	245 0.6×	65 0.3×	78 0.5×	25	661
Theodor Bröcker Germany	6	455 0.7×	205 0.5×	480 1.2×	117 0.6×	262 1.6×	10	1.1k

Countries citing papers authored by Grant Cairns

Since Specialization

Citations

This map shows the geographic impact of Grant Cairns's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Grant Cairns with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Grant Cairns more than expected).

Fields of papers citing papers by Grant Cairns

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Grant Cairns. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Grant Cairns. The network helps show where Grant Cairns may publish in the future.

Co-authorship network of co-authors of Grant Cairns

This figure shows the co-authorship network connecting the top 25 collaborators of Grant Cairns. A scholar is included among the top collaborators of Grant Cairns based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Grant Cairns. Grant Cairns is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

1.

Cairns, Grant, et al.. (2016). Conewise Linear Periodic Maps of the Plane with Integer Coefficients. American Mathematical Monthly. 123(4). 363–375. 3 indexed citations

2.

Cairns, Grant, et al.. (2015). Great-circle spherical thrackles. Discrete Mathematics. 338(12). 2507–2513. 1 indexed citations

3.

Cairns, Grant, et al.. (2015). A sharp refinement of a result of Zverovich–Zverovich. Discrete Mathematics. 338(7). 1085–1089. 4 indexed citations

4.

Cairns, Grant, et al.. (2015). Wolstenholme again. Elemente der Mathematik. 70(3). 125–130. 1 indexed citations

5.

Cairns, Grant, et al.. (2011). The Sprague–Grundy function of the real game Euclid. Discrete Mathematics. 311(6). 457–462. 7 indexed citations

6.

Cairns, Grant, et al.. (2010). Utimately bipartite subtraction games. Australas. J Comb.. 48. 213–220. 1 indexed citations

7.

Cairns, Grant, et al.. (2009). Topological transitivity of solvable group actions on the line R. Colloquium Mathematicum. 116(2). 203–215.

8.

Cairns, Grant, et al.. (2008). Free submodules for the central representation in the cohomology of Lie algebras. Proceedings of the American Mathematical Society. 136(6). 1919–1923.

9.

Cairns, Grant, et al.. (2008). Catalan numbers, primes, and twin primes. Elemente der Mathematik. 63(4). 153–164. 2 indexed citations

10.

Cairns, Grant, et al.. (2007). Brussels Sprouts and Cloves. Mathematics Magazine. 80(1). 46–58. 1 indexed citations

11.

Cairns, Grant, et al.. (2007). An example of a chaotic group action on Euclidean space by compactly supported homeomorphisms. Topology and its Applications. 155(3). 161–164. 1 indexed citations

12.

Cairns, Grant. (2005). Is there a greater role for prime numbers in our schools. 19(1). 24–37. 1 indexed citations

13.

Cairns, Grant, et al.. (2003). Cohomology operations for Lie algebras. Transactions of the American Mathematical Society. 356(4). 1569–1583. 3 indexed citations

14.

Cairns, Grant, et al.. (2001). All odd musquashes are standard. Discrete Mathematics. 226(1-3). 71–91. 2 indexed citations

15.

Cairns, Grant, et al.. (1999). The answer to Woodall's musquash problem. Discrete Mathematics. 207(1-3). 25–32. 2 indexed citations

16.

Brown, Gavin, et al.. (1997). JAZ volume 62 issue 1 Cover and Front matter. Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics. 62(1). f1–f3. 1 indexed citations

17.

Cairns, Grant, et al.. (1996). Chaotic actions of free groups. Nonlinearity. 9(4). 1015–1021. 16 indexed citations

18.

Cairns, Grant, et al.. (1993). A new formula for winding number. Geometriae Dedicata. 46(2). 149–159. 15 indexed citations

19.

Cairns, Grant. (1990). Totally umbilic Riemannian foliations.. The Michigan Mathematical Journal. 37(1). 6 indexed citations

20.

Cairns, Grant. (1986). A general description of totally geodesic foliations. Tohoku Mathematical Journal. 38(1). 13 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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