Patrick M. Gilmer

763 total citations
34 papers, 413 citations indexed

About

Patrick M. Gilmer is a scholar working on Geometry and Topology, Mathematical Physics and Discrete Mathematics and Combinatorics. According to data from OpenAlex, Patrick M. Gilmer has authored 34 papers receiving a total of 413 indexed citations (citations by other indexed papers that have themselves been cited), including 32 papers in Geometry and Topology, 23 papers in Mathematical Physics and 6 papers in Discrete Mathematics and Combinatorics. Recurrent topics in Patrick M. Gilmer's work include Geometric and Algebraic Topology (28 papers), Homotopy and Cohomology in Algebraic Topology (23 papers) and Algebraic structures and combinatorial models (11 papers). Patrick M. Gilmer is often cited by papers focused on Geometric and Algebraic Topology (28 papers), Homotopy and Cohomology in Algebraic Topology (23 papers) and Algebraic structures and combinatorial models (11 papers). Patrick M. Gilmer collaborates with scholars based in United States and France. Patrick M. Gilmer's co-authors include Charles Livingston, Gregor Masbaum and R. A. Litherland and has published in prestigious journals such as Communications in Mathematical Physics, Transactions of the American Mathematical Society and Inventiones mathematicae.

In The Last Decade

Patrick M. Gilmer

31 papers receiving 337 citations

Peers — A (Enhanced Table)

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

Name	h						Papers	Cites
Patrick M. Gilmer United States	13	365	301	86	60	37	34	413
S. Yu. Orevkov France	11	273 0.7×	112 0.4×	78 0.9×	68 1.1×	49 1.3×	49	310
Yoshiyuki Yokota Japan	12	316 0.9×	208 0.7×	64 0.7×	141 2.4×	23 0.6×	25	327
Jeffrey L. Tollefson United States	11	368 1.0×	266 0.9×	74 0.9×	77 1.3×	77 2.1×	45	410
J. Scott Carter United States	10	568 1.6×	404 1.3×	123 1.4×	230 3.8×	24 0.6×	26	596
José María Montesinos-Amilibia Spain	10	245 0.7×	197 0.7×	43 0.5×	83 1.4×	51 1.4×	37	307
Nathan M. Dunfield United States	9	289 0.8×	236 0.8×	50 0.6×	99 1.6×	17 0.5×	17	312
Bert Wiest France	10	255 0.7×	183 0.6×	96 1.1×	75 1.3×	12 0.3×	24	296
Wilbur Whitten United States	9	191 0.5×	145 0.5×	54 0.6×	44 0.7×	32 0.9×	25	230
Daniel Ruberman United States	12	388 1.1×	340 1.1×	50 0.6×	65 1.1×	82 2.2×	45	421
Andrew Casson United States	8	647 1.8×	546 1.8×	97 1.1×	138 2.3×	131 3.5×	10	698

Countries citing papers authored by Patrick M. Gilmer

Since Specialization

Citations

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

Fields of papers citing papers by Patrick M. Gilmer

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Patrick M. Gilmer. 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 Patrick M. Gilmer. The network helps show where Patrick M. Gilmer may publish in the future.

Co-authorship network of co-authors of Patrick M. Gilmer

This figure shows the co-authorship network connecting the top 25 collaborators of Patrick M. Gilmer. A scholar is included among the top collaborators of Patrick M. Gilmer 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 Patrick M. Gilmer. Patrick M. Gilmer 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

Gilmer, Patrick M. & Charles Livingston. (2016). Signature jumps and Alexander polynomials for links. Proceedings of the American Mathematical Society. 144(12). 5407–5417. 3 indexed citations

Gilmer, Patrick M. & Gregor Masbaum. (2007). Integral lattices in TQFT. Annales Scientifiques de l École Normale Supérieure. 40(5). 815–844. 18 indexed citations

Gilmer, Patrick M.. (2004). Integrality for TQFTs. Duke Mathematical Journal. 125(2). 14 indexed citations

Gilmer, Patrick M.. (2003). The Kauffman bracket skein module of the quaternionic manifold. Civil War Book Review. 6 indexed citations

Gilmer, Patrick M., et al.. (2000). Real Algebraic Geometry and Ordered Structures. Contemporary mathematics - American Mathematical Society. 22 indexed citations

Gilmer, Patrick M.. (1999). Quantum invariants of periodic three-manifolds. Geometry and topology monographs. 157–175. 4 indexed citations

Gilmer, Patrick M.. (1999). On the Witten-Reshetikhin-Turaev representations of mapping class groups. Proceedings of the American Mathematical Society. 127(8). 2483–2488. 10 indexed citations

Gilmer, Patrick M.. (1999). Topological Quantum Field Theory and Strong Shift Equivalence. Canadian Mathematical Bulletin. 42(2). 190–197. 5 indexed citations

Gilmer, Patrick M.. (1997). Invariants for one-dimensional cohomology classes arising from TQFT. Topology and its Applications. 75(3). 217–259. 10 indexed citations

10.

Gilmer, Patrick M.. (1996). Turaev-Viro Modules of Satellite knots. 2 indexed citations

11.

Gilmer, Patrick M.. (1993). Classical knot and link concordance. Commentarii Mathematici Helvetici. 68(1). 1–19. 17 indexed citations

12.

Gilmer, Patrick M. & Charles Livingston. (1992). The Casson-Gordon invariant and link concordance. Topology. 31(3). 475–492. 24 indexed citations

13.

Gilmer, Patrick M. & Charles Livingston. (1992). Discriminants of Casson–Gordon invariants. Mathematical Proceedings of the Cambridge Philosophical Society. 112(1). 127–139. 17 indexed citations

14.

Gilmer, Patrick M.. (1992). Real algebraic curves and link cobordism. Pacific Journal of Mathematics. 153(1). 31–69. 11 indexed citations

15.

Gilmer, Patrick M.. (1991). Algebraic Curves in RP(1) × RP(1). Proceedings of the American Mathematical Society. 113(1). 47–47.

16.

Gilmer, Patrick M. & R. A. Litherland. (1986). The duality conjecture in formal knot theory. Osaka Journal of Mathematics. 23(1). 229–247. 5 indexed citations

17.

Gilmer, Patrick M.. (1984). Ribbon concordance and a partial order on S-equivalence classes. Topology and its Applications. 18(2-3). 313–324. 11 indexed citations

18.

Gilmer, Patrick M. & Charles Livingston. (1983). On embedding 3-manifolds in 4-space. Topology. 22(3). 241–252. 40 indexed citations

19.

Gilmer, Patrick M.. (1982). On the slice genus of knots. Inventiones mathematicae. 66(2). 191–197. 16 indexed citations

20.

Gilmer, Patrick M.. (1981). Topological proof of theG-signature theorem forGfinite. Pacific Journal of Mathematics. 97(1). 105–114. 24 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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