A. Duane Randall

• Biographical Information
• Publications and Books
• Teaching
• Contact Information

• Rev. John Keller, S. J. Distinguished Professor of Mathematics in the Department of Mathematics and Computer Science under College of Humanities and Natural Sciences

• Ph.D. from the University of California, Berkeley, 1968.

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• "Some Immersion Theorems for Projective Spaces."  Transactions of the American Mathematical Society.  Vol. 147, Jan. 1970, pp. 135-151.  MR 40 #6572.
• "Some Immersion Theorems for Manifolds."  Transactions of the American Mathematical Society Vol. 156, May, 1971, pp. 45-58.  MR 44 #3335.
• "Note on the Generalized Vector Field Problem."  Boletin de la Sociedad Matematica Mexicana.  Vol. 17, Oct. 1972, pp 40-41.  MR 48 #12554.
• "Projectivity of the Whitehead Square."  Proceedings of American Mathematical Society.  Vol. 40, Oct. 1973, pp. 609-611.  MR 50 #8518.
• "Cohomology of Quasi-Projective Stiefel Manifolds." Rocky Mountain Journal of Mathematics.  Vol. 3, 1973, pp. 619-630.  MR 49 #8048.
• "F-Projectivity of the Whitehead Square."  Anais da Academia Brasileira de Ciencias.  Vol. 2, 1975, pp. 29-31.  MR 54 #3697.
• "F-Projective Homotopy and F-Projective Stable Stems."  Duke Mathematical Journal.  Vol. 12, 1975, pp. 99-104.  MR 52 #1690.
• "Note on Self-Mappings of Quaternionic Projective Spaces."  With Howard Marcum.  Anais da Academia Brasileira de Ciencias.  Vol. 48, 1976, pp. 7-9.   MR 55 #9086.
• "Remarks on Vector Fields."  Proceedings of the Tenth Brazilian Mathematics Colloquium.  Vol. 2, 1978, pp. 441-446.  MR 82g: 57010.
• "Tangent Frame Fields on Spin Manifolds."  Pacific Journal of Mathematics.  Vol. 76, 1978, pp. 157-167.  MR 58 #7650.
• "A Classe de Thom em Homotopia e Ciclica?"  Proceedings of Eleventh Brazilian Mathematics Colloquium.  Vol. 2, 1978, p. 779.
• "The Homotopy Thom Class of a Spherical Fibration."  With Howard Marcum.   Proceedings of the American Mathematical Society.  Vol. 80, 1980, pp. 353-358.   MR 81R: 55026.
• "Index of Vector Fields with Finite Singularities."  Proceedings of the Twelfth Brazilian Mathematics Colloquium.  Vol. 2, 1981, pp. 641-647.
• "Index of Tangent Fields on Compact Manifolds."   With J. L. Arraut.   Contemporary Mathematics.  Vol. 12, 1982.  American Mathematical Society, pp. 31-46.  MR 83m: 57018.
• "Some Properties of Whitehead Squares."  Atlas of First Brazilian Topology Reunion.  Sociedade Brasileira de Matematica, 1981, pp. 109-117.
• "The Parallelizable Property for Closed Manifolds."  Atlas of Second Brazilian Topology Reunion.  Universidade de Sao Paulo, 1982, pp. 89-92.
• "On Equivariant Maps of Stiefel Manifolds."  Proceedings of AMS Conference on Group Actions on Manifolds.  Contemporary Mathematics.  Vol. 36, American Mathematical Society, 1985, pp. 145-149.  MR 86c: 57031.
• "On Sectioning Vector Bundles."  Atlas of Third Brazilian Topology Reunion.  Universidade de Sao Paulo, 1985, pp. 67-76.
• "Recent Results on Immersing Projective Spaces."  Atlas of Fourth Brazilian Topology Reunion, Universidade de Sao Paulo, 1985, pp. 77-82.
• "CAT 2-Fields on Nonorientable CAT Manifolds."  Quarterly Journal of Mathematics.  Oxford (2), 38 (1987), pp. 355-366.  MR 88j: 57022.
• "Tangent 2-Fields on Closed Manifolds."  Proceedings of the Fifteenth Brazilian Mathematics Colloquium.  Sociedade Brasileira de Matematica, 1987, pp. 369-373.
• "On Indices of Tangent Fields with Finite Singularities."  Differential Topology, Second Siegen Symposium.  Lecture Notes in Mathematics, Vol. 1350, Springer-Verlag, pp. 213-240, 1988.  MR 90e: 57052.
• "On Equivariant Maps and Immersions of Projective Spaces."  With Jon Berrick.  Algebraic Topology, Arcata 1986.  Lecture Notes in Mathematics, Vol. 1370, 1989.  Springer-Verlag, pp. 57-62.  Mr 90c: 57024.
• "On 4-Manifolds and Span-Related Numbers for CAT Manifolds."  Manuscripta Mathematica 69 (1990), pp. 339-351.  MR 91j: 57020.
• "On Splitting Topological R4-Bundles."  With Carl H. Brans.   Topology and its Applications 43 (1992), pp. 37-45.  MR 93d: 57053.
• "Low Dimensional Spinor Representations, Adams Maps and Geometric Dimension."   With Kee Lam.  Adams Memorial Symposium on Algebraic Topology. London Math.   Society Lecture Note Series 175 (1992), pp. 89-102.  Cambridge University Press.  MR 93f: 55019.
• "Exotic Differentiable Structures and General Relativity."  With Carl Brans.  General Relativity and Gravitation 25 (1993), pp. 205-221.  MR 94g: 57038.
• "On Foliations, Concordance Spaces, and the Smale Conjectures."  With Paul A. Schweitzer, S.J. Differential Topology, Foliations and Group Actions.   Contemporary Mathematics, Vol. 161, American Mathematical Society, 1994, pp. 235-258.   MR 95a: 57031.
• "On 4-Dimentional Bundle Theories."  Differential Topology, Foliations, and Group Actions.  Contemporary Mathematics, Vol. 161, American Mathematical Society, 1994, pp. 217-233.  95b: 57023.
• "Geometric Dimension of Bundles on Real Projective Spaces."  With Kee Lam.  Homotopy Theory and its Applications.  Contemporary Mathematics, Vol. 188, American Mathematical Society, 1995, pp. 137-160.  MR 97c: 55030.
• "Periodicity of Geometric Dimension for Real Projective Spaces."  With Kee Lam.  Algebraic Topology: New Trends in Localization and Periodicity.   Progress in Mathematics, Vol. 136, Birkhauser Verlag, 1996, pp. 223-234.  MR 97d: 55030.
• "On Oriented Bundle Theories and Applications."  Geometric Topology: Proceedings of the Georgia International Conference on Geometry and Topology. AMS/IP Studies in Advanced Mathematics, Vol. 2, American Mathematical Society, 1997, pp. 446-455.   MR 98g: 57042.
• "Projectivity of ImJ, Cospherical Classes and Geometric Dimension."  With Kee Lam.  Stable and Unstable Homotopy.  Communications Volume of the Fields Institute for Research.  American Mathematical Society, Vol. 19, pp. 181-186, 1998. MR 99b: 55025.
• "Block Bundle Origin of Stable Block Bundle Homotopy."  Contemporary Mathematics, Vol. 227, American Mathematical Society, 1999, pp. 287-302. MR 99k: 55018.
• "Embedding Homotopy Spheres and the Kervaire Invariant."   Homotopy Invariant Algebraic Structures. Contemporary Mathematics, Vol. 239, American Mathematical Society, 1999, pp. 239-243. MR 2000h: 57062.
• Aihua Li and Duane Randall, "Non-trivial Solutions to Certain Matrix Equations." Electronic Journal of Linear Algebra 9, 2002, pp. 282-289. MR 2004a: 15020.
• Duane Randall, "Equivalences to the Triangulation Conjecture. " Algebraic and Geometric Topology 2, 2002, pp. 1147-1154. MR 2003i: 57032.
• Nancy de Souza Cardim, Maria Herminia de P. L. Mello, Duane Randall and Mario Olivero Marques da Silva, "Join Products and Indices of k-fields over Differentiable Fiber Bundles. " Topology and its Applications 136, 2004, pp. 275-291. MR 2004i: 55019.
• Daciberg Gonçalves and Duane Randall, "Self-coincidence of Maps from S^q-Bundles over S^n to S^n. " Boletin de la Sociedad Matematica Mexicana, Vol. 10, Special Issue, 2004, pp. 181-192.
• Kee Lam and Duane Randall, "Vector Bundles of Low Geometric Dimension over Real Projective Spaces. " Mathematical Proceedings of the Cambridge Philosophical Society, 139 (2005), no. 2, 229-241.
• Kee Yuen Lam and Duane Randall, "Block Bundle Obstruction to Kervaire Invariant One." Recent Developments in Algebraic Topology, 163-171, Contemporary Mathematics, 407, American Mathematical Society, Providence, RI 2006. MR2248977.
• Daciberg Gonçalves and Duane Randall, "Self-coincidence of mappings between spheres and the Strong Kervaire Invariant One Problem." Comptes Rendus Mathematique, C. R. Acad. Sci. Paris 342 (2006), no. 7, 511-513. MR2006m:55033.

Books

• D. Randall and J. Daccach.  Sequencias Espectrais, Espacos de Eilenberg-MacLane, Torres de Postnikov.  The University of Sao Paulo in Sao Carlos.  September, 1988.   69 pages.

• D. Randall and J. Daccach.  Cobordismo Normal e Aplicacoes.   The University of Sao Paulo in Sao Carlos.  September, 1988.  53 pages.

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Loyola University, New Orleans

• Math A257-001, Calculus I.
• Math A257-002, Calculus I.
• Math A401-001, Abstract Algebra II.

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Contact Information

E-mail:    randall@loyno.edu

Fax:    504-865-2051

Office Phone:    504-865-3342

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