Paul Melvin

1.0k total citations
29 papers, 476 citations indexed

About

Paul Melvin is a scholar working on Geometry and Topology, Mathematical Physics and Computational Theory and Mathematics. According to data from OpenAlex, Paul Melvin has authored 29 papers receiving a total of 476 indexed citations (citations by other indexed papers that have themselves been cited), including 24 papers in Geometry and Topology, 22 papers in Mathematical Physics and 5 papers in Computational Theory and Mathematics. Recurrent topics in Paul Melvin's work include Geometric and Algebraic Topology (22 papers), Homotopy and Cohomology in Algebraic Topology (12 papers) and Advanced Operator Algebra Research (7 papers). Paul Melvin is often cited by papers focused on Geometric and Algebraic Topology (22 papers), Homotopy and Cohomology in Algebraic Topology (12 papers) and Advanced Operator Algebra Research (7 papers). Paul Melvin collaborates with scholars based in United States, United Kingdom and Canada. Paul Melvin's co-authors include Robion Kirby, H. R. Morton, Nicholas Tufillaro, John F. Hughes, Charles Livingston, Tim D. Cochran, Daniel Ruberman, William Kazez, Xingru Zhang and Jeffrey B. Parker and has published in prestigious journals such as Physical Review A, Communications in Mathematical Physics and Inventiones mathematicae.

In The Last Decade

Paul Melvin

27 papers receiving 409 citations

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
Paul Melvin United States	11	420	345	150	44	39	29	476
Denis Auroux United States	13	440 1.0×	324 0.9×	77 0.5×	34 0.8×	22 0.6×	24	468
Sergei Chmutov United States	10	297 0.7×	163 0.5×	204 1.4×	20 0.5×	91 2.3×	24	351
Darryl McCullough United States	13	496 1.2×	404 1.2×	123 0.8×	27 0.6×	71 1.8×	59	548
François Labourie France	15	531 1.3×	450 1.3×	62 0.4×	41 0.9×	39 1.0×	36	655
Nathan Habegger France	10	488 1.2×	460 1.3×	113 0.8×	11 0.3×	68 1.7×	25	536
Lev Borisov United States	12	315 0.8×	211 0.6×	69 0.5×	66 1.5×	29 0.7×	40	373
Richárd Rimányi United States	11	379 0.9×	244 0.7×	210 1.4×	60 1.4×	46 1.2×	41	412
Peter Teichner United States	14	604 1.4×	559 1.6×	131 0.9×	14 0.3×	109 2.8×	48	648
Jean Cerf	4	297 0.7×	274 0.8×	36 0.2×	27 0.6×	49 1.3×	8	385
Jean-Pierre Otal France	13	435 1.0×	410 1.2×	71 0.5×	47 1.1×	45 1.2×	23	534

Countries citing papers authored by Paul Melvin

Since Specialization

Citations

This map shows the geographic impact of Paul Melvin'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 Paul Melvin with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Paul Melvin more than expected).

Fields of papers citing papers by Paul Melvin

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Paul Melvin. 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 Paul Melvin. The network helps show where Paul Melvin may publish in the future.

Co-authorship network of co-authors of Paul Melvin

This figure shows the co-authorship network connecting the top 25 collaborators of Paul Melvin. A scholar is included among the top collaborators of Paul Melvin 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 Paul Melvin. Paul Melvin 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

Melvin, Paul & Hannah Schwartz. (2020). Higher order corks. Inventiones mathematicae. 224(1). 291–313. 1 indexed citations

Melvin, Paul, et al.. (2017). Equivariant corks. Algebraic & Geometric Topology. 17(3). 1771–1783. 5 indexed citations

DeTurck, Dennis, et al.. (2013). Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows. Journal of Mathematical Physics. 54(1). 6 indexed citations

DeTurck, Dennis, et al.. (2013). Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows, part II. Algebraic & Geometric Topology. 13(5). 2897–2923. 1 indexed citations

Friedl, Stefan, Ian Hambleton, Paul Melvin, & Peter Teichner. (2007). Non-smoothable Four-manifolds with Infinite Cyclic Fundamental Group. International Mathematics Research Notices. 2007. 3 indexed citations

Melvin, Paul, et al.. (2005). The nonuniqueness of Chekanov polynomials of Legendrian knots. Geometry & Topology. 9(3). 1221–1252. 12 indexed citations

Kirby, Robion & Paul Melvin. (2004). Local surgery formulas for quantum invariants and the Arf invariant. Geometry and topology monographs. 213–233. 8 indexed citations

Melvin, Paul, et al.. (2001). A Geometric Interpretation of Milnor's Triple Invariants. Algebraic & Geometric Topology. 1 indexed citations

Cochran, Tim D. & Paul Melvin. (2001). Quantum cyclotomic orders of 3-manifolds. Topology. 40(1). 95–125. 10 indexed citations

10.

Melvin, Paul & H. R. Morton. (1995). The coloured Jones function. Communications in Mathematical Physics. 169(3). 501–520. 58 indexed citations

11.

Kirby, Robion & Paul Melvin. (1994). Dedekind sums, ?-invariants and the signature cocycle. Mathematische Annalen. 299(1). 231–267. 39 indexed citations

12.

Melvin, Paul & Nicholas Tufillaro. (1991). Templates and framed braids. Physical Review A. 44(6). R3419–R3422. 30 indexed citations

13.

Kirby, Robion & Paul Melvin. (1991). The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C). Inventiones mathematicae. 105(1). 473–545. 184 indexed citations

14.

Melvin, Paul & Jeffrey B. Parker. (1986). 4-Manifolds with large symmetry groups. Topology. 25(1). 71–83. 4 indexed citations

15.

Melvin, Paul. (1984). 2-sphere bundles over compact surfaces. Proceedings of the American Mathematical Society. 92(4). 567–572. 5 indexed citations

16.

Livingston, Charles & Paul Melvin. (1983). Algebraic Knots are Algebraically Dependent. Proceedings of the American Mathematical Society. 87(1). 179–179. 7 indexed citations

17.

Livingston, Charles & Paul Melvin. (1983). Algebraic knots are algebraically dependent. Proceedings of the American Mathematical Society. 87(1). 179–180. 6 indexed citations

18.

Melvin, Paul. (1982). Tori in the diffeomorphism groups of simply-connected 4-manifolds. Mathematical Proceedings of the Cambridge Philosophical Society. 91(2). 305–314. 5 indexed citations

19.

Melvin, Paul. (1981). On 4-manifolds with singular torus actions. Mathematische Annalen. 256(2). 255–276. 8 indexed citations

20.

Melvin, Paul. (1979). Bordism of diffeomorphisms. Topology. 18(2). 173–175. 8 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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