Papers of Henry C. King

Articles on Topology of Singularities

• Real Analytic Germs and Their Varieties at Isolated Singularities, Inventiones Mathematicae, Vol. 37 (1976), pp. 193-199, MR 54 #13114. Note: this paper has an error in an example which was corrected in the paper by Les Reid, A correction to a paper of H. King, Invent. Math. 88 (1987), no. 2, pp. 423-425, MR #89a:57040
• The Number of Critical Points in Morse Approximations, Compositio Mathematica, Vol. 34 (1977), pp. 285-288, MR 56 #1330
• Topological Type of Isolated Critical Points, Annals of Math., Vol. 107 (1978), 385-397, MR 58#13081
• Topological Type in Families of Germs, Inventiones Math., Vol. 62 (1980), 1-13, MR #83a:58014
• Local behavior of Morse functions on Singular Spaces (ps file) I think this is a writeup of a talk I gave in Georgia in 1990?
• Topology of Isolated Critical Points of Functions on Singular Spaces, Stratifications and Topology of Singular Spaces II, Collection Travaux en Cours 55, Hermann (1997), pp. 63-72. (ps file)
• Sums of Isolated Critical Points (dvi file), preprint

Articles on Topology of Real Algebraic Varieties

• Approximating Submanifolds of Real Projective Space by Varieties, Topology, Vol. 15 (1976), pp. 81-85, MR 53 #435
• (with S. Akbulut) Real Algebraic Structures on PL Manifolds, BAMS, Vol. 83 (1977), pp. 281-282, MR 55 #13434
• (with S. Akbulut) The Topology of Real Algebraic Sets with Isolated Singularities, Annals of Math., Vol. 113 (1981), 425-446, MR #83b:58003
• (with S. Akbulut) Real Algebraic Structures on Topological Spaces, Publ. I.H.E.S., Vol. 53 (1981), 79-162, MR #83h:58009
• (with S. Akbulut) A Relative Nash Theorem, TAMS, Vol. 267 (1981), 465-481, MR #83b:58004
• (with S. Akbulut) All Knots are Algebraic, Comm. Math. Helv., Vol. 56 (1981), 339-351, MR #83m:57005
• (with S. Akbulut) A Topological Characterization of Real Algebraic Varieties, BAMS, Vol. 2 (1982), pp. 171-173, MR #82a:57017
• The Topology of Real Algebraic Sets, Proceedings of the AMS Summer Institute on Singularities, Arcata, Proc. Symp. Pure Math., 40, AMS (1983), MR #85i:14013
• (with S. Akbulut) The Topology of Real Algebraic Sets, L'Enseignement Math., t. 29 (1983), p. 221-261, MR #86d:14016a
• Survey on the topology of real algebraic sets, Rocky Mountain Journal of Math., Vol. 14 (1984), p. 821-830, MR #86d:14017
• (with S. Akbulut) Submanifolds and Homology of Nonsingular Real Algebraic Varieties, American Journal of Math., Vol. 107 (1985), p. 45-84, MR #86m:14017
• (with S. Akbulut) A Resolution Theorem for Homology of Real Algebraic Varieties, Inventiones Math., 79 (1985), p. 589-601, MR #86g:14011
• (with S. Akbulut) The Topology of Resolution Towers, TAMS, 302 (1987), p. 497-521, MR #88g:57039
• (with S. Akbulut) Introduction to Resolution Towers, 1985 Georgia Topology Conference, Lecture Notes in Pure and Applied Mathematics 105, Dekker, 1987, MR #87m:57040
• (with S. Akbulut) Polynomial Equations of Immersed Surfaces, Pacific Journal of Math., 131 (1988), p. 209-217, MR #89c:57028
• (with S. Akbulut) Some new results on the Topology of Nonsingular Real Algebraic Sets, BAMS, Vol. 23 (1990), pp. 441-446, MR #91e:57034
• (with S. Akbulut) Rational Structures on 3-manifolds, Pacific Journal of Math., 150 (1991), pp. 201-214, MR #93c:57028
• (with S. Akbulut) All compact manifolds are homeomorphic to totally algebraic real algebraic sets, Comm. Math. Helv., 66 (1991), pp. 139-149, MR #92c:14056
• (with S. Akbulut) Topology of Real Algebraic Sets, MSRI publications, Vol. 25, Springer-Verlag (1992). errata, MR #94m:57001
• (with S. Akbulut) On approximating submanifolds by algebraic sets and a solution to the Nash Conjecture, Inventiones Math., 107 (1992), pp. 87-98, MR #93d:57051
• (with S. Akbulut) Algebraicity of immersions in $R^n$, Topology, 31 (1992), pp. 701-712, MR #94d:57055
• Topological Properties Arising from Real Algebraic Geometry, Topology Hawaii, World Scientific (1992), pp. 149-156, MR #93e:57063
• (with S. Akbulut) Constructing Strange Real Algebraic Sets, Real Algebraic Geometry, Proceedings, Rennes 1991, Lecture Notes in Mathematics 1524, Springer-Verlag (1992), pp. 120-127. (ps file) , MR #94c:14046
• (with S. Akbulut) Trancendental Submanifolds of $R^n$ , Commentarii Math. Helv., 68 (1993), pp. 308-318, MR #94j:57032
• Resolving Singularities of Maps, Real Algebraic Geometry and Topology, AMS Contemporary Mathematics, Vol. 182,(1995), pp. 135-154. (ps file) , MR #96e:14016
• (with S. Akbulut) On Algebraic Vector Bundles, Real Algebraic Geometry and Topology, AMS Contemporary Mathematics, Vol. 182, (1995). (ps file) , MR #96e:57015
• (with J. Calcut) Real Algebraic Interiors and a problem of Arnol'd, Michigan Mathematics Journal. 52 (2004), pp. 361-373. (pdf file)
• (with S. Akbulut) Transcendental submanifolds of RP^n, Commentarii Mathematici Helvetici. 80, 2, pp. 427-432.
• Tico Spines, arXiv:1602.02608 [math.GT]. This gives the details of a proof of an elementary result used in The Topology of Real Algebraic Sets with Isolated Singularities, but only gave a picture proof there.

Articles on Intersection Homology

• Intersection Homology and Homology Manifolds, Topology, Vol. 21 (1982), 229-234, MR #83j:57010
• Topological Invariance of Intersection Homology without Sheaves, Topology and Applications, 20 (1985), p. 149-160, MR #86m:55010

Articles on Linkages

• Planar Linkages and Algebraic Sets, arXiv:math/9807023 [math.AG]
• Semiconfiguration Spaces of Planar Linkages, arXiv:math/9810130 [math.GT]
• Configuration Spaces of Linkages in R^n, arXiv:math/9811138 [math.GT]
• Connected Projections of Configuration Spaces of Linkages, arXiv:1812.10370 [math.MG]

Articles on Computational Topology

• (with K. Knudson and N. Mrarmor) Generating discrete Morse functions from point data, Experimental Mathematics 14 (2005). The algorithm in this article is implemented in this tarball or for older versions, see here.
  
• (with K. Knudson and N. Mrarmor) Birth and death in discrete Morse theory, J. Symbolic Comput. 78 (2017), 41-60, arXiv:0808.0051 [math.AT]. The algorithm in this article is implemented in this tarball.

Articles on other things

• (with D. Trotman) Poincare-Hopf Theorems on Singular Spaces, Proceedings of the London Math. Soc., (2014) 108 (3), pp. 682-703. (ps file)
• (with D. Geiger, D. Heckerman, C. Meek), Stratified Exponential Families: Graphical Models and Model Selection, Annals of Statistics, 29 (2001), no.~1, pp. 505-529.
• (with D. Geiger, D. Heckerman, C. Meek), On the geometry of DAG models with hidden variables, (link)
• (with J. Calcut and L.Siebenmann) Connected Sum at Infinity and Cantrell-Stallings hyperplane unknotting, Rocky Mountain Journal of Mathematics 42 (2012), pp. 1803-1862 arXiv:1010.2707 [math.GT]
  
• Morse Cells, arXiv:1610.07509 [math.GT]

Last modified, April 22, 2021

Comments and questions to hking@math.umd.edu