The home page of   Gerard A. Venema
Professor of Mathematics at Calvin College
Associate Secretary of the Mathematical Association of America

List of Publications

Journal Articles

  1. Embeddings of compacta with shape dimension in the trivial range, Proceedings of the American Mathematical Society, vol. 55 (1976), pages 443 - 448 [MR53 #1596].
  2. Weak flatness for shape classes of sphere-like continua, General Topology and its Applications, vol. 7 (1977), pages 309 - 319 [MR56 #9535 ].
  3. A topological disk in a 4-manifold can be approximated by piecewise linear disks, Bulletin of the American Mathematical Society, vol. 83 (1977), pages 386 - 387 [MR55 #4192].
  4. Approximating disks in 4-space, Michigan Mathematical Journal, vol. 25 (1978), pages 19 - 26.
  5. A topological embedding which cannot be approximated by piecewise linear embeddings, Notices American Mathematical Society, vol. 24 (1977), page A-302 (with W. T. Eaton and C. P. Pixley).
  6. A weak-flattening criterion for compacta in 4-space, in Geometric Topology, ed. by J. C. Cantrell, Academic Press, New York, 1979 (with T. B. Rushing) [MR#80h:57022].
  7. Neighborhoods of compacta in Euclidean space, Fundamenta Mathematicae, vol. 109 (1980), pages 71 - 78 [MR#382d:57006].
  8. Failure of the Dehn Lemma on contractible 4-manifolds, Inventiones mathematicae, vol. 51 (1979), pages 205 - 218 (with Y. Matsumoto) [MR#80k:57013].
  9. The fundamental dimension of embedding, in Proceedings of the International Conference on Geometric Topology, Polish Scientific Publishers, Warsaw, 1980.
  10. An approximation theorem in shape theory, Topology and its Applications, vol. 14 (1982), pages 111 - 116 [MR#83h:55018].
  11. Approximating topological surfaces in 4-manifolds, Transactions of the American Mathematical Society, vol. 265 (1981), pages 35 - 45 [MR#82i:57022].
  12. Complement theorems beyond the trivial range, Illinois Journal of Mathematics, vol. 25 (1981), pages 209 - 220 (with I. Ivanšić and R. B. Sher) [MR#82i:57017].
  13. The Whitney trick in dimension four, Russian Mathematical Surveys, vol. 35 (1980), pages 193 - 195 [also translated into Russian and published in Uspekhi Matematicheskikh Nauk, Tom 35 (1980), pages 157 - 158] [MR#82d:57009].
  14. Embeddings in shape theory, in Shape Theory and Geometric Topology, ed. by S. Mardešić and J. Segal, Springer-Verlag, New York, 1981 [MR#83a:57019].
  15. Approximating topological embeddings of cells in codimension two, Pacific Journal of Mathematics, vol. 126 (1987), pages 165 - 195 [MR#88g:57027].
  16. Homotopy equivalences on 3-manifolds, Proceedings of the American Mathematical Society, vol. 91 (1984), pages 637 - 642 [MR#85m:57010].
  17. Stable shape concordance implies homeomorphic complements, Fundamenta Mathematicae, vol. 126 (1986), pages 123 -131 (with Vo Thanh Liem) [MR#87h:57021].
  18. Embeddings of locally connected compacta, Transactions of the American Mathematical Society, vol. 292 (1985), pages 613 - 627 [MR#87i:57018].
  19. CE equivalence and shape equivalence of 1-dimensional compacta, Topology and its Applications, vol. 26 (1987), pages 131 - 142 (with R. J. Daverman) [MR#89b:57012].
  20. CE equivalences in the locally connected category, Journal of the London Mathematical Society, ser. (2) vol. 35 (1987), pages 169 - 176 (with R. J. Daverman) [MR#88a:55011].
  21. Finite dimensional complement theorems: examples and results, Proceedings of the American Mathematical Society, vol. 103 (1988), pages 299 - 306 (with R. B. Sher) [MR#89f:57027].
  22. Neighborhoods of compacta in 4-manifolds, Topology and its Applications, vol. 31, (1989), pages 83 - 99 [MR#90a:57023].
  23. A new proof of the trivial range complement theorem, preprint, 1988.
  24. Concordance of compacta, Compositio Mathematica, vol. 75 (1990), pages 193 - 201 (with Vo Thanh Liem) [MR# 91g:57018].
  25. Neighborhoods of S1-like continua in 4-manifolds, Michigan Mathematical Journal, vol. 40 (1993), pages 3 - 25 (with Fredric Ancel and Vo Thanh Liem) [MR#95c:57035].
  26. Characterization of knot complements in the 4-sphere, Topology and its Applications, vol. 42 (1991) pages 231 - 245 (with Vo Thanh Liem) [MR#92k:57045].
  27. Characterization of knot complements in the 4-sphere: a special case, Proceedings of the Sixth Annual Workshop in Geometric Topology, pages 65 - 68 (with Vo Thanh Liem).
  28. Complements of 2-spheres in 4-manifolds (with Vo Thanh Liem), in Topology Hawaii, World Scientific Publishing Co., Singapore (1992), pages 157 - 164 [MR#93h:57033].
  29. On the asphericity of knot complements (with Vo Thanh Liem), Canadian Journal of Mathematics, vol. 45 (1993), pages 340 - 356 [MR#93m:57027].
  30. Cell-like images and UVm groups, Topology and its Applications, vol. 50 (1993), pages 35 - 46 [MR#94c:55019].
  31. Duality on non-compact manifolds and complements of topological knots, Proceedings of the American Mathematical Society, vol. 123 (1995), pages 3251 - 3262 [MR#96b:57012].
  32. Characterization of knot complements in the n-sphere, Fundamenta Mathematicae, vol. 147 (1995), pages 189 - 196. (with Vo Thanh Liem) [MR#96g:57028].
  33. Local homotopy properties of topological embeddings in codimension two, in Topology of Manifolds, edited by Will Kazez, Studies in Advanced Mathematics, vol. 2, published by the American Mathematical Society and International Press, 1996, pages 388 - 405 [MR#98d:57036].
  34. Homotopy groups of complements of topological knots, Proceedings of the 1993 Workshop in Geometric Topology, pages 68 - 70.
  35. A manifold that does not contain a compact core, Topology and its Applications, vol. 90 (1998), pages 197 - 210 [MR#99k:57046].
  36. A homotopy equivalence that is not homotopic to a topological embedding, (with Vo Thanh Liem and Yukio Matsumoto) Topology and its Applications, vol. 90 (1998), pages 211 - 222 [MR#99m:57019].
  37. A 4-dimensional shrinking theorem, (with M. Bestvina, R. J. Daverman, and J. Walsh), Topology and its Applications, vol. 110 (2001), pages 3 - 20.
  38. Representing homology classes of 4-manifolds (with Vo Thanh Liem), Topology and its Applications, vol. 120 (2002), pages 57 - 65.
  39. The mathematics of T. Benny Rushing, Topology and its Applications, vol. 120 (2002), pages 1 - 7.
  40. Classifying polygonal chains of six segments (with Tom Clark), Journal of Knot Theory and its Ramifications, vol. 13 (2004), pages 479 - 514.
  41. Constructing PL 2-sphere complements (with Jon Dent and John Engbers), to appear in the Proceedings of the 22nd Annual Workshop in Geometric Topology, Colorado College, June, 2005.

Other Publications

  1. Weak Flatness for Shape Classes, Doctoral Dissertation, University of Utah, Salt Lake City, Utah, 1975.
  2. The Foundations of Geometry, a textbook for an undergraduate course in axiomatic geometry. Published by Prentice Hall, Upper Saddle River, NJ, 2005, 452 pages.
  3. The Foundations of Geometry, Second Edition. Published by Pearson Education, Inc., Boston, MA, 2012.
  4. Proceedings of the 19th Annual Workshop in Geometric Topology. I served as editor for these informally published proceedings; a printed copy of the volume may be obtained by contacting me (venema@calvin.edu). The complete proceedings may be downloaded as a sequence of pdf documents by clicking here.
  5. Embeddings in Manifolds, a book being written with Robert J. Daverman. The book will be published by the American Mathematical Society in the Graduate Studies in Mathematics series.
  6. Exploring Advanced Euclidean Geometry with GeoGebra. Published by the Mathematical Association of Americia, Washington DC, 2013. An inquiry-based introduction to advanced Euclidean geometry that utilizes the open source software package GeoGebra. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry.

Student Publications

  1. Knots in Four Dimensions and the Fundamental Group, by Jeff Boersema and Erica Whitaker, Rose Hulman Undergraduate Mathematics Journal, vol. 4, Issue 2, 2003.
  2. Classifying polygonal chains of six segments by Tom Clark and Gerard Venema, Journal of Knot Theory and its Ramifications, vol. 13 (2004), pages 479 - 514.
  3. Classifying polygonal chains of six segments by Tom Clark and Gerard Venema, Undergraduate Research Highlights, Council on Undergraduate Research Quarterly, vol. 25, September, 2004, page 8.
  4. New models for hyperbolic geometry, by Tom Clark, Senior Thesis, Calvin College, 2004.
  5. 4-manifolds, Kirby calculus, and the construction of knotted 2-spheres in 4-space, by Jonathan Dent and John Engbers, to be submitted for publication in the Rose Hulman Undergraduate Mathematics Journal.

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