Uwe Kaiser's research page

My address: Department of Mathematics, Boise State University, 1900 University Drive, Boise, Idaho 83725

email: ukaiser@boisestate.edu

My research interests are in Geometric topology. I consider myself a Differential Topologist interested in all problems related to manifolds. These are questions of immersions and embeddings. I am interested in link theory in manifolds and in low dimensions in associated geometric and quantum invariants. I am also interested in all aspects of Quantum Computing. Here are some questions I am presently working on or interested in: Categorification of invariants of links in 3-manifolds (LMO-invariant, skein modules); Geometry of skein modules; Computation of quantum invariants in low-dimensional topology; representations of fundamental groups of 3-manifolds.

Selected presentations

  1. Rokhlin seminar (St. Petersburg, Russia, 05-17-2021) A survey of Bar-Natan skein theory
  2. Geometric topology seminar (Moscow, Russia, 04-30-2021) String topology and homotopy skein modules
  3. Joint AMS/MAA Meeting (2021, online, 01-06-2021) Kashaev and extended Kauffman summation; slides
  4. Knots in Washington XLIX (Washington DC, 02-09-2020) Kashaev invariant and Kauffman states; abstract
  5. CUNY Einstein Chair Seminar (New York, 04-23-2002) Skein modules and 3-manifolds

I am also giving regularly talks in Boise State’s Department of Mathematics TATERS seminar.


  1. A short survey of quantum computing; Journal of Knot Theory and it Ramifications 26, 2017, no.3, 19 pp.
  2. On the construction of generalized skein modules; Knots in Poland III, Part 1, Banach Center Publications 100, Polish Acad. Sci. Inst. Math., Warsaw, 2014
  3. Frobenius algebras and skein modules of surfaces in 3-manifolds; Algebraic Topology – old and new, 59-81, Banach Center Publications 85, Polish Acad. Sci. Inst. Math., Warsaw, 2009
  4. (with Nikos Apostolakis) Kauffman state sums and bracket deformation; Journal of Knot Theory and its Ramifications 16 (2007), no. 7, 809-831
  5. Link bordism skein modules; Fundamenta Mathematicae 184 (2004), 113-134
  6. Quantum deformations of fundamental groups of oriented 3-manifolds; Transactions of the AMS 356 (2004), 3869-3880
  7. Deformation of string topology into homotopy skein modules; Algebraic and Geometric Topology 3, 2003, no. 34, 1005-1035
  8. Presentations of q-homotopy skein modules of oriented 3-manifolds; Journal of Knot Theory and its Ramifications Vol. 10, No. 3 (May 2001), 461-491
  9. Link theory in manifolds; Lecture Notes in Mathematics 1669, 167 pp., Springer Verlag, Berlin 1997
  10. (with Nathan Habegger) Link homotopy in the 2-metastable range; Topology 37, No. 1, 1998, 75-93
  11. (with Nathan Habegger) Homotopy classes of two disjoint 2p-spheres in R^3p+1; Topology and its Applications 71, 1996, 1-8
  12. Link homotopy and skein modules; in Proceedings of the AMS-Israel Joint Workshop at Haifa, Contemp. Math Vol. 164, 1994, 59-77
  13. Homology boundary links and strong fusion; Osaka Journal of Mathematics 29, 1992, 573-593
  14. Geometric properties of strong fusion; Journal of Knot theory & its ramifications, Vol. 1, No. 3, 1992, 297-302
  15. Strong bandsum and dichromatic invariants; Manuscripta Mathematica 74, 1992, 317-336
  16. Bands, tangles and linear skein theory; Manuscripta Mathematica 71, 1991, 317-336
  17. Link homotopy in R^3 and S^3; Pacific Journal of Mathematics, Vol. 151, No. 2, 1991, 257-264
  18. (with Li Banghe) On the reflection of immersions in Euclidean space; Acta Mathematica Sinica, Vol. 11, No. 3, 1991, 257-264
  19. Verschlingungsabbildungen im Euklidischen Raum, Zentralblatt review; PhD thesis University of Siegen, 1989
  20. (with Li Banghe) Enumeration of immersions of m-manifolds in (2m-2)-manifolds; in Differential Topology, Proceedings, Siegen 1987, Lecture Notes in Mathematics Vol. 1350, Springer Verlag 1988, 171-188
  21. Immersions in codimension 1 up to regular homotopy; Archiv der Mathematik, Vol. 51, 1998, 371-377

STEM Education research: (with Louis S. Nadelson, Sharon McGuire, Kimberly Hardy, Kisten A. Davis, Arvin Farid and Yu-Chang Hsu) Am I a STEM Professional? Documenting STEM student professional identity development; Studies in Higher Education, July 2015

ArXiv & MATH Reviews & etc

  1. ArXiv Papers
  2. My Papers reviewed in Math Reviews
  3. My zbMATH entry
  4. My Math Reviews
  5. My zbMATH reviews
  6. Selected Works, Boise State University
  7. My CV