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Vita Publications & Preprints K-Presentations Slides of Recent Talks Theses

Curriculum Vitae (pdf-file 93 kB)

Publications and Preprints

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	"Resolutions of p-Modular TQFT's and Representations of Symmetric Groups". (submitted) 29 pages. math.GT/0110006
	"p-Modular TQFT's, Milnor Torsion, and the Casson-Lescop Invariant". Geom. Topol. Monogr. 4 (2002) 119-141. math.GT/0203256
	"Homology TQFT's and the Alexander-Reidemeister Invariant of 3-Manifolds via Hopf Algebras and Skein Theory". *Canad. J. Math.* 55 (2003) 766-821. (38 figures). math.GT/0008204
	"Towards an Algebraic Characterization of 3-dimensional Cobordisms". Contemp. Math. 318 (2003) 141-173. (66 figures) math.GT/0106253
	"Non-semisimple Topological Quantm Field Theories for 3-Manifolds with Corners". *Lecture Notes in Mathematics* 1765, Springer Verlag, 2001 vi + 376 pp. ISBN: 3-540-42416-4, over 200 illustrations (with V. Lyubashenko). Read here Introduction, Anstract and Contents.
	"Integration on Braided Hopf Algebras". J. Pure Appl. Algebra . 148 (2000), no. 2, 113-164. (with Y.Bespalov, V.Lyubashenko, V.Turaev) q-alg/9709020
	"Bridged Links and Tangle Presentations of Cobordism Categories". Adv. Math. 141 (1999), no. 2, 207-281. math.GT/9806114
	"Equivalence of a Bridged Link Calculus and Kirby's Calculus of Links on Non-simply Connected 3-Manifolds". *Topology Appl.* 87 (1998) 155-162 . math.GT/9806113
	"On the connectivity of cobordisms and half-projective TQFT's". Comm. Math. Phys. 198 (1998), no. 3, 535-590. q-alg/9603017
	"Genealogy of Nonperturbative Quantum-Invariants of 3-Manifolds: The Surgical Family". `Geometry and Physics', Lecture Notes in Pure and Applied Physics 184, Marcel Dekker (1996) 503-547. q-alg/9601021
	"Mapping Class Group Actions on Quantum Doubles". Comm. Math. Phys. 168 (1994) 353-388. hep-th/9402017
	"Quantumgroups, Quantumcategories and Quantumfieldtheory" *Lecture Notes in Mathematics* 1542, Springer Verlag, 1993 viii + 431 pp. $65.00. ISBN: 3-540-56623-6. Second Printing, 1995. (with J.Fröhlich)
	"On braided tensorcategories". Differential geometric methods in theoretical physics (Ixtapa-Zihuatanejo, 1993). Adv. Appl. Clifford Algebras 4 (1994), Suppl. 1, 49-60. hep-th/9402018.
	"Non-Tannakian categories in quantum field theory". New symmetry principles in quantum field theory (Cargèse, 1991), 449-482, NATO Adv. Sci. Inst. Ser. B Phys. 295, Plenum, New York, 1992.
	"Structuring the Set of Incompressible Quantum Hall Fluids". Nucl. Phys. B 453 (1995) 670-704.(with J.Fröhlich, U.Studer, E.Thiran)
	"Non-Abelian Bosonization in Two Dimensional Condensed Matter Physics" Nucl. Phys. B 374 (1992) 511-542. (with J.Fröhlich, P.A. Marchetti)
	"Universality in Quantum Hall Systems" Nucl. Phys. B 354 (1991) 369-417 (with J.Fröhlich)
	"Darstellungen der Quantegruppen und Anwendungen", Diplomarbeit, ETH-Zürich, 1989.

K-Presentations
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Topological Quantum Field Theorie. (4.7 MB)
Mar/25/2004 Colloquium, Math Dept. Louisiana State, Baton Rouge, LA

Integral TQFT's and the Torelli Groups. (2.6 MB)
Jan/9/2004 Joint Mathematics Meeting, Phoenix, AZ.

Block Property of Integral TQFT's. (2.8 MB)
Dec/19/2003 Knots in Washington XVII, Washington, DC

2+1 dim TQFT's over Cyclotomic Integers (3.2 MB)
Nov/14/2003 Math Dept. UC San Diego, San Diego, CA.

Why is the Poincare Sphere not a Sphere (3.1MB)
Oct/15/2003 Math Club at Ohio State, Columbus, OH

Slides of Recent Talks << back to top of page



Jan/18/03: Baltimore, MD (Convent. Ctr.)	**.ps.gz-file (122kB) .pdf-file (217kB)**
*On TQFT Realizations of the* *Johnson-Morita Homomorphism*	AMS National Meeting #983
Nov/10/02: U.C.F., Orlando, FL	**.ps.gz-file (121kB) .pdf-file (392kB)**
*Some Computations for* *"Width=2" TQFT's*	AMS Sectional Meeting #982
Aug/12/02: Shaanxi Normal Univeristy, Xi'an CHINA	**.ps.gz-file (151kB) .pdf-file (451kB)**
*The Fibonacci and other* *Cyclotomic Integer TQFT's*	Geometric Topology A Satellite Conference of ICM 2002
Jun/21/02: P.S.U., Portland, OR	**.ps.gz-file (963kB) .pdf-file (5.47MB)**
*Applications of Quantum* *Invariants of 3-Manifold*	AMS Sectional Meeting #978
Mar/19/02: M.R.C . Warwick, U.K.	**.ps.gz-file (697kB) .pdf-file (781kB)**
*Search for* Finite Length TQFT's:	Workshop "Quantum Topology" 3/2002
Mar/2/02: Univ.of Mich., Ann Arbor, MI	**.ps.gz-file (241kB) .pdf-file (242kB)**
*Finite Length TQFT's*	AMS Sectional Meeting #974
Sep/6/01: R.I.M.S. Kyoto, JAPAN	**.ps.gz-file (291kB) .pdf-file (861kB)**
*p-Modular TQFT's* *and Torsion*	Workshop "Invaraints of knots and 3-manifolds"

Master's Thesis

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Craig Jackson: Braid Group Representations(Ohio State University, 2001)

Work in Progress


`The Krammer Lawrence Representations via $U_q({\mathfrak s}{\mathfrak l}_2)$''. (joint with Craig Jackson)
``On the Structure of the Fibonacci TQFT's over $\Z[\zeta_5]$''
``Cut Numbers of 3-manifolds via quantum orders in $\Z[\zeta_5]$'' (joint with Pat Gilmer).
``Asymptotics of the Turaev-Viro Invariant'' (joint with Charlie Frohman).
``Mutation Invariance for Quantum Invariants''. (joint Yongwu Rong).