A. Duane Randall
Biographical
Information
-
Ph.D. from the University of California, Berkeley, 1968.
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Research
Papers and Books
- "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.
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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.
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Duane Randall, "Equivalences to the Triangulation Conjecture.
" Algebraic and Geometric Topology 2, 2002, pp. 1147-1154.
MR 2003i: 57032.
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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.
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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.
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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.
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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.
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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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Teaching
Spring 2007
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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This portion of the website was last updated on
Thursday, December, 14, 2006.