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J. Scott Carter

J. Scott Carter

Professor Emeritus

Department of Math and Statistics

Education

B.S. March 1978, Summa Cum Laude,
University of Georgia, Athens, Georgia,
Mathematics Major
Ph.D. in Mathematics, May 1982
Yale University, New Haven, Connecticut
Dissertation: "Surgery on Immersions: a Geometric Approach to Stable Homotopy," Advisor Prof. Ronnie Lee.

Publications

J. Scott Carter Published Articles ...

with Seung Yeop Yang,
with Yongju Bae, Seonmi Choi, and Sera Kim,
with Seiichi Kamada, Three dimensional braids and their descriptions, special issue of Topology and Its Applications, International Conference on Topology and Geometry 2013, the Sixth Japan-Mexico Topology
with Daniel Silver and Susan Williams. Invariants of links in thickened surfaces, Algebr. Geom. Topol. 14 (2014), no. 3, 1377 1394.
with Daniel Silver and Susan Williams. Three dimensions of knot coloring, Amer. Math. Monthly 121 (2014), no. 6, 506 514.
with Seiichi Kamada : How to fold a manifold, to appear in New Ideas in Low Dimensional Topology, ed. Kauffman and Manturov.

Books

, with Seiichi Kamada, Mathematical Surveys and Monographs Volume: 264; American Mathematical Society (Providence 2021)
, World Scientific Publishing, Singapore (First edition 1993), (Second edition 1995)
with D.E. Flath and M. Saito, Princeton University Press (1995).
, with Masahico Saito American Mathematical Society.
, with Masahico Saito and Seiichi Kamada, Springer-Verlag.
, with Seiichi Kamada, Lou Kauffman, Akio Kawauchi, and Toshitake Kohno
, World Science Publishing, Series on Knots and Everything, Volume 48.

More articles published by J. Scott Carter

, to appear in New Ideas in Low Dimensional Topology, ed. Kauffman and Manturov.
with Atsushi Ishii. . Published in unrefereed conference Proceedings, Intelligence of Low Dimensional Topology, RIMS.
with Seiichi Kamada: , Published in unrefereed conference Proceedings, Intelligence of Low Dimensional Topology, RIMS, with Seiichi Kamada.
, Symmetry (2012), 4, 225-250.
, preprint, to appear in conference proceedings of Trieste form May 2009.
with Masahico Saito, , preprint.
with Masahico Saito, , to appear J. Gen. Lie Theory Appl.
with Masahico Saito and Kanako Oshiro, Topology Appl. 157 (2010), no. 5, 857-869.
with Abhijit Champanerkar, , preprint.
with Alissa Crans, Mohamed Elhamdadi, Masahico Saito, , preprint.
with Alissa Crans, Mohamed Elhamdadi, Masahico Saito, , Journal of Homotopy Theory and Related Structures 3 (2008), no. 1, 13-63.
with Alissa Crans, Mohamed Elhamdadi, Masahico Saito, . J. Gen. Lie Theory Appl. 2 (2008), no. 1, 19--34.
with Masahico Saito, Cohomology for self-distributivity in coalgebras. Intelligence of low dimensional topology 2006, 9--17, Ser. Knots Everything, 40, World Sci. Publ., Hackensack, NJ, 2007.
with Masahico Saito, Shin Satoh, . Proc. Amer. Math. Soc. 134 (2006), no. 9, 2779--2783.
with Masahico Saito, . J. Knot Theory Ramifications 15 (2006), no. 8, 949--956.
with Mohamed Elhamdadi, Shin Satoh and Masahico Saito, , Topology Appl. 153 (2006), no. 15, 2788--2794.
with Shin Satoh and Masahico Saito, , J. Aust. Math. Soc. 80 (2006), no. 1, 131--147.
with Mohamed Elhamdadi, Matias Grana, and Masahico Saito, Cocycle knot invariants from quandle modules and generalized quandle homology. Osaka J. Math. 42 (2005), no. 3 499--541.
with Mohamed Elhamdadi and Masahico Saito, Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles. Fund. Math. 184 (2004), 31--54.
with Masahico Saito. . Topology and geometry of manifolds (Athens, GA, 2001), 249--268, Proc. Sympos. Pure Math., 71, Amer. Math. Soc., Providence, RI, 2003.
with Masahico Saito and Seiichi Kamada, . Diagrammatic morphisms and applications (San Francisco, CA, 2000), 51--74, Contemp. Math., 318, Amer. Math. Soc., Providence, RI, 2003.
with Mohamed Elhamdadi, Angela Harris, Marina Nikiforou and Masahico Saito, Cocycle knot invariants, quandle extensions, and Alexander matrices. Low-dimensional topology of tomorrow (Japanese) (Kyoto, 2002).
with Shin Satoh, Masahico Saito and Seiichi Kamada, Bordism of unoriented surfaces in 4-space. Michigan Math. J. 50 (2002), no. 3, 575--591.
with Masahico Saito and Seiichi Kamada, Knots 2000 Korea, Vol. 1 (Yongpyong). J. Knot Theory Ramifications 11 (2002), no. 3, 311--322.
with Mohamed Elhamdadi, and Masahico Saito, . Algebr. Geom. Topol. 2 (2002), 95--135.
with Shin Satoh, Masahico Saito and Seiichi Kamada, , Algebr. Geom. Topol. 1 (2001), 299--310.
with Daniel Jelsovsky, Masahico Saito and Seiichi Kamada, . J. Knot Theory Ramifications 10 (2001), no. 4, 579--596.
with Daniel Jelsovsky, Masahico Saito and Seiichi Kamada, . J. Knot Theory Ramifications 10 (2001), no. 3, 345--386.
with Daniel Jelsovsky, Masahico Saito and Seiichi Kamada, . J. Pure Appl. Algebra 157 (2001), no. 2-3, 135--155.
with Daniel Jelsovsky, Masahico Saito and Seiichi Kamada, . Adv. Math. 157 (2001), no. 1, 36--94.
with Daniel Jelsovsky, Masahico Saito, Seiichi Kamada, and Laurel Langford, . Trans. Amer. Math. Soc. 355 (2003), no. 10, 3947--3989.
with Louis H. Kauffman and Masahico Saito, Structures and Diagrammatics of 4-Dimensional Topological Lattice Field Theories, Advances in Math., 146, 39-100 (1999).
with Masahico Saito and Seiichi Kamada, Alexander numbering of knotted surface diagrams, Proc. Amer. Math. Soc., 128 (2000), no. 12, 3761--3771.
with Masahico Saito and Vera Carrara, Singularities of Surface Maps and Knots, Pacific J. Math. 199 (2001), no. 1, 21--40.
with Sostenes Lins, Thin-G theory and local moves for gems, Adv. Math. 143 (1999), no. 2, 251--283. Advances in Mathematics, 127, No. 1, April 15 (1997), 1-51.
with Louis H. Kauffman and Masahico Saito, Diagrammatics, Singularities, and Their Algebraic Interpretations, 10th Brazilian Topology Meeting (S茫o Carlos, 1996). Mat. Contemp. 13 (1997), 21--115.
with Masahico Saito, Surfaces in 3-Space that Do Not Lift to Embeddings in 4-Space, to appear in Conference Proceedings of the 1995 Warsaw Workshop on Knot Theory.
with Masahico Saito, and Joachim Rieger, , Advances in Mathematics, 127, No. 1, April 15 (1997), 1-51.
with Masahico Saito, Normal Euler Classes of Knotted Surfaces and Triple Points on Their Projections, Proc. Amer. Math. Soc., 125 (1997), no. 2, 617-623.
with Masahico Saito, , International Journal of Modern Physics A, Vol 11, No 24, (1996), 4453-4463.
with Masahico Saito, Braid and Movies, Journal of Knot Theory and Its Ramifications, Vol 5, No. 5 (1996), 589-608.
with Masahico Saito, A Seifert Algorithm for Knotted Surfaces, Topology, Vol 36, No. 1 (1996), 179-201.
with Masahico Saito, Knot Diagrams and Braid Theories in Dimension 4 Real and Complex Singularities, ed. W. L Marar, Pitman Research Notes in Mathematics, Longman Publishing (1995).
with Masahico Saito, New Solutions to the Permutohedron Equation in ``Quantum Topology Kansas 1993,'' ed. David Yetter, World Science Publishing Company (1994), 51-65.
with Masahico Saito, Knotted Surfaces, Braid Movies, and Beyond, in ``Quantum Gravity,'' ed. John Baez, Oxford University Press (1994), 191-229.
with Masahico Saito, Reidemeister Moves for Surface Isotopies and Their Interpretations As Moves to Movies, Journal of Knot Theory and its Ramifications Vol 2, No 3 (1993), 251-284.
Solving Inequalities, Alabama Journal of Mathematics, Vol 1, No.1 \& 2, (1992), 31-35.
with Masahico Saito, A Diagrammatic Theory of Knotted Surfaces, in ``Quantum Topology,'' ed. Randy Baadhio and Louis Kauffman, World Science Publishing (Singapore 1993), 91-115.
with Masahico Saito, Planar Generalizations of the Yang Baxter Equation and Their Skeins, Journal of Knot Theory and its Ramifications Vol 1, No. 2 (1992), 207-217.
with Masahico Saito, Syzygies among Elementary String Interactions in Dimension 2+1, Letters in Mathematical Physics 23 (1991), 287-300.
Extending Immersed Circles in the Sphere to Immersed disks in the Ball, Comm. Math. Helv. 67 (1992), 337-348.
with Masahico Saito, Canceling Branch Points on Projections of Surfaces in 4-Space, Proc. of the AMS. 116, No 1. (Sept 1992), 229-237.
Closed Curves that Never Extend to Proper Maps of Disks, Proc. of the AMS 113, No. 3 (Nov 1991), 879-888.
Extending Immersed Curves to Proper Immersions of Surface, Topology and its Applications 40 (1991), 287-306.
Classifying Immersed Curves, Proc. of the AMS 111, No.1 (Jan. 1991), 281-287.
Immersed Projective Planes in Lens Spaces, Proc. of the AMS 106, No. 1 (May 1989), 251-260.
Immersed Codimension One Projective Spaces in Spherical Space Forms, Proc. of the AMS 105, No. 1, January 1989, 254-257.
with Ki Hyoung Ko, Triple Points of Immersed Surfaces in Three Dimensional Manifolds, Topology and Its Applications 32, (1989), 149-159.
Surgery on the Equatorial Immersion in Low Dimensions, Differential Topology Proceedings, Siegen 1987, Springer LMN 1350, U. Koschorke, ed.
Surgery on the Equatorial Immersion I, Illinois Journal of Mathematics 32, No. 4, Winter 1988, 703-715.
Simplifying the Self Intersection Sets of Codimension One Immersions in (n+1)-space, Houston Journal of Mathematics 13, No. 3, 353-366.
A Further Generalization of Boy's Surface, Houston Journal of Mathematics 12, No. 1 (1986), 11-31.
On Generalizing Boy's Surface: Constructing a Generator of the Third Stable Stem, Trans. of the AMS 289, No. 1 (1986), 103-121.
, Trans. of the AMS 298, No. 1, (1986), 83-102.
Surgery Theory of Immersions, Proc. Northwestern Homotopy Theory Conf. (Miller and Priddy, eds.), AMS Contemp. Math Series 19 (1983), 23-37.