Thomas Banchoff's Research-Oriented Articles
- Tightly embedded 2-dimensional polyhedral
manifolds, Amer. J. Math., 87 (1965), 462-472.
(abstract)
(
AMS review #31#2729)
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Critical points and curvature for embedded polyhedra, J. Differential Geometry, 1 (1967), 257-268. (abstract)
(
AMS review #85b:53061)
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Total central curvature of curves, Duke Math. J., 37 (1970), 281-289. (abstract)
(
AMS review #41#4447)
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Periodic points of Anosov diffeomorphisms (with Michael I. Rosen), Proceedings of
Symposia in Pure Mathematics, Global Analysis, Vol. XIV (1970), 17-21.(abstract)
(
AMS review #43#2738)
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The spherical two piece property and tight surfaces in spheres, J. Differential Geometry, 4 (1970), 193-205.
(abstract)
(
AMS review #42#3720)
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Critical points and curvature for embedded polyhedral surfaces, Amer. Math. Monthly, 77 (1970), 475-485.
(
AMS review #41#4444)
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Non-rigidity theorems for tight polyhedral tori, Archiv der Mathematik, 21 (1970), 416-423. (abstract)
(
AMS review #42#8426)
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The two-piece property and tight n-manifolds-with-boundary in E^n , Trans. Amer. Math. Soc. 161 (1971), 259-267.
(abstract)
(
AMS review #44#4760)
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[9] On a generalization of the isoperimetric inequality
(with William Pohl), J. Differential
Geometry, 6 (1971), 175-192.
(
AMS review #46#4449)
- High codimensional 0-tight mappings on spheres, Proc. Amer. Math. Soc., 29 (1971), 133-137.
(abstract)
(
AMS review #43#5541)
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Polyhedral Catastrophe I: Maps of the Line to the Line, Dynamical Systems, Academic
Press (1973), 7-22.
(
AMS review #49#6268)
- Foliations of Knot Complements in the Bicylinder
Boundary, Separata do Boletim da Sociedade Brasileira de
Matematica Vol. 5, No. 1 (1974), pp. 31-43.
(abstract)
- Global Geometry of Polygons I: The Theorem of Fabricius-Bjerre, Proc. A.M.S. 45 (1974), 237-241.
(abstract)
(
AMS review #51#6826)
- Tight Polyhedral Klein Bottles, Projective Planes, and
Mobius Bands, Math. Ann. 207 (1974), pp. 233-243.
(abstract)
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Triple Points and Surgery for Immersed Surfaces, Proc. A.M.S. 46 (1974), 407-413.
(abstract)
- abstract)
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Stiefel-Whitney Homology Classes and Singularities of Projections for Polyhedral Manifolds, Amer. Math. Soc. Proc. Sympos. Pure Math., Vol. XXVII, Stanford University 1973, Part I (1975), 333-347.
(abstract)
(
AMS review #51#14090)
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The Behavior of the Total Twist and Self-Linking Number of a Closed Space Curve under Inversions (with James E. White), Mathematica Scandinavica 36 (1975), 254- 262. (abstract)
(
AMS review #52#4312)
- Height functions with three critical points (with Floris Takens), Illinois J. Mathematics, 76 (1975), 325-335.
(abstract)
(
AMS review #51#14079)
- Minimal submanifolds of the Bicylinder Boundary ,Boletim da Sociedade Brasileira de
Matematica, 7 (1976), 37-57.
(
AMS review #58#12844)
- Self-Linking Numbers of Space Polygons, Indiana University Mathematics Journal 25
(1976), 1171-1188. (abstract)
(
AMS review #55#4227)
- Immersions and Mod 2 Quadratic Forms (with Lou Kauffman), American Mathematical
Monthly 84 (1977), 168-185. (Awarded Lester Ford Award for exposition, Summer 1978). (abstract)
(
AMS review #55#4210)
- Whitney Duality and Singularities of Projections (with Clint McCrory), Proceedings of
Escuela Latino-americana de Mathematica, Rio de Janeiro, Springer-Verlag Lecture Notes in Mathematics 5997 (1977), 68-81.
(
AMS review #56#6678)
- Combinatorial Formula for Normal Stiefel-Whitney
Classes (with Clint McCrory), Proceedings of the A.M.S.
76 (1979), 171-177.
(abstract)
- Selected Papers in Geometry (Edited by Ann Stehney, Tilla Milnor, Joseph D'Atri and Thomas Banchoff), Mathematical Association of America (1979).
(
AMS review #82c:01041)
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Sur les points paraboliques des surfaces: erratum et complements (with Rene Thom), C. R. Acad. Sc. Paris, 291 (27 Octobre 1980), 503-505.
- Every Sphere Eversion has a Quadruple Point (with Nelson Max), Am. J. Math.,
Supplementary Issue (1981), 191-209.
(abstract)
(
AMS review #83g:57020)
- Cusps of Gauss Mappings (with T. Gaffney and C. McCrory), Pitman Advanced Publishing Program, 55 (1982), London, pp. 1-88.
(abstract)
- Frenet Frames and Theorem of Jacobi and Milnor for
Space Polygons, Jugoslavenska Akademija Znanosti I Umjetnosti , iz
Rada 396 (1982), pp. 101-108.
(abstract)
- Double Tangency Theorems for Pairs of Submanifolds, Geometry Symposium Utrecht
(1980), Springer-Verlag Lecture Notes 894, pp. 26-48.
(
AMS review #83h:53005)
- Geometrical Class and Degree for Surfaces in Three-Space (N. Kuiper), J. Diff. Geom. 16 (1981), 559-576.
(abstract)
(
AMS review #83j:53056)
- Circular and Countercircular Images of Plane Curves (with E. Beckenbach), General
Inequalities 3 (1983), ISNM64, Birkhäuser-Verlag, 321-337.
(abstract)
(
AMS review #86h:53003)
- The Nine-Vertex Complex Projective Plane (with W. Kühnel), Mathematical Intelligencer 5 (1983), 11-22.
(abstract)
(
AMS review #85d:51016)
- Linear Algebra Through Geometry (with J. Wermer), Springer-Verlag (1983).
(
AMS review #84f:15001)
- DIAL: A Diagrammatic Animation Language (with S. Feiner and D. Salesin), IEEE
Computer Graphics and Applications, 2, No. 7 (1982), 43-54.
- Critical points and curvature for embedded polyhedra II,
Differential Geometry, Proc.
Special Year, Maryland, Progress in Math 32, BirkhŠuser (1983), 34-55.
(abstract)
- La Quarta Dimensio i Salvador Dali,
Breu Viatge al mon de la Mathematica, 1 (1984),
pp. 19-24.
- Normal Curvatures and Euler Classes for
Polyhedral Surfaces in 4-Space,
Proc. A.M.S.,92 (1984), 593-596.
(abstract)
(
AMS review #86c:57019)
- Counting Tritangent Planes of Space Curves (with T. Gaffney and C. McCrory), Topology 34 (1985), 15-24.
(abstract)
(
AMS review #86m:58028a)
- Visualizing Two-Dimensional Phenomena in Four-Dimensional Space, Statistical Image Processing, Marcel Dekker (1986), 187-202.
(abstract)
(
AMS review #89a:58001)
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Topology and Mechanics with Computer Graphics: Linear
Hamiltonian Systems in Four Dimensions (with H. Koçla;ak, F. Bisshopp and D. Laidlaw), Advances in Applied
Mathematics (1986), 282-308.
(abstract)
(
AMS review #88a:58069)
- Global Theorems for Symmetry Sets of Smooth
Curves and Polygons in the Plane (with Peter Giblin)
Proc. Royal Soc. Edinburgh 106A (1987) 221-231.
(
AMS review #88j:53003)
- Torus Decompositions of Regular Polytopes
in 4-Space. Shaping Space (1988), Birkhäuser-Verlag, 221-230.
(
AMS review #937 089)
- Geometry of the Hopf Mapping and Pinkall's
Tori of Given Conformal Type
Computers in Geometry, Marcel Dekker, New York (1990) 57-62.
(abstract)
(
AMS review #90c:53035)
- Linear Algebra Through Geometry (with J. Wermer), revised and expanded second edition, Springer-Verlag (1991).
- Euler Numbers, Complex Points and
Singularities of Projections for Oriented Surfaces in Four-Space
(with F. Farris) Pacific Journal of Mathematics 161
no. 1 (1993) 1, 24..
- Equilibrium Triangulations of the Complex
Projective Plane (with Wolfgang Kühnel), Geometriae
Dedicata. 44(1992)313-333.
(abstract)
(
AMS review #94a:52035)
- Symmetry Sets of Piecewise Circular Curves
(with Peter Giblin), Proc. Royal Soc. Edinburgh
123A (1993) 1-15.
(abstract)
(
AMS review #95a:58007)
- Tangential and Normal Euler Numbers,
Complex Points, and Singularities of Projections for Oriented
Surfaces in Four-Space (with Frank Farris), Pacific Journal of
Mathematics Vol. 161 No. 1. (1993) pp. 1-24.
(abstract)
- On the Geometry of Piecewise Circular Curves
(with Peter Giblin), American Mathematical Monthly 101
No. 5 (1994) 403-416.
(abstract)
(
AMS review #95k:51030a)
- Circumscribing Conics around Convex Quadrilaterals
(with Philip J. Davis)
(abstract)