Gregor Masbaum

Institut de Mathématiques de Jussieu (UMR 7586 du CNRS) Equipe Topologie et Géométrie Algébriques email : (please remove the letters x,y, and z) masxyzbaum@math.jussieu.fr Bureau: Campus Jussieu, Tour 16-26, 5e étage, pièce 506 Téléphone: (+33) 1 44 27 86 81 Adresse postale : Institut de Mathématiques de Jussieu (UMR 7586 du CNRS) Equipe Topologie et Géométrie Algébriques Case 247 4 pl. Jussieu 75252 Paris Cedex 5

Programme

Prépublications / Preprints

(with P. M. Gilmer) Irreducible factors of modular representations of mapping class groups arising in Integral TQFT. Revised Version 30 Oct. 2012, see also arXiv:1110.5666

(with P. M. Gilmer) Dimension formulas for some modular representations of the symplectic group in the natural characteristic. Journal of Pure and Applied Algebra 217 (2013), 82-86 arXiv:1111.0240

(with A. W. Reid) All finite groups are involved in the Mapping Class Group. Geometry & Topology 16 (2012) 1393-1411 arXiv:1106.4261 Final Version for Geometry & Topology

(with P. M. Gilmer) Maslov index, Lagrangians, Mapping Class Groups and TQFT. Forum Mathematicum (to appear) arXiv:0912.4706

(with S. Caracciolo, A. Sokal, A. Sportiello.) A randomized polynomial-time algorithm for the spanning hypertree problem on 3-uniform hypergraphs, Preprint, also available as arXiv:0812.3593

Publications

(with P. M. Gilmer) Integral TQFT for a one-holed torus. Pac. J. Math. 252 (2011) No. 1, 93-112 Journal version ArXiv version: arXiv:0908.2796

(with M. Loebl) On the optimality of the Arf invariant formula for graph polynomials. Advances in Mathematics 226 (2011) 332-349. arXiv:0908.2925

On representations of mapping class groups in Integral TQFT. Oberwolfach Reports, Volume 5, Issue 2, 2008, pp. 1157-1232. Preprint version

(with P. M. Gilmer) Integral Lattices in TQFT. Ann. Sci. École Norm. Sup. 40 (2007) 815-844 Preprint version (PDF, 450K), also available as math.QA/0411029.

(with J. E. Andersen and K. Ueno) Topological Quantum Field Theory and the Nielsen-Thurston classification of M(0,4). Math. Proc. Cam. Phil. Soc. 141 (2006) 477-488 Preprint version (March 2005) (postscript, 520K) also available as math.GT/0503414.

(with P. M. Gilmer and P. van Wamelen) Integral bases for TQFT modules and unimodular representations of mapping class groups. Comment. Math. Helv. 79 (2004) 260-284. Preprint (version: July 2002) (gzipped postscript, 229 K), also available as math.QA/0207093. Journal version

Quantum representations of mapping class groups. In: Groupes et Géométrie. Journée annuelle 2003 de la SMF. pages 19-36 Fichier PDF (222K)

Skein-theoretical derivation of some formulas of Habiro. Algebraic and Geometric Topology 3 (2003) 537-556. Preprint (gzipped postscript, 196K).

(with A. Vaintrob) Milnor numbers, Spanning Trees, and the Alexander-Conway Polynomial. Advances in Mathematics 180 (2003), no. 2, 765--797. Preprint (version: October 2001) (gzipped postscript, 156 K), also available as math.GT/0111102.

Matrix-tree theorems and the Alexander-Conway polynomial. In: Invariants of knots and 3-manifolds (Kyoto 2001), Geometry and Topology Monographs, Vol. 4 (2002), 201--214. Preprint (gzipped postscript, 171 K).

(with A. Vaintrob) A New Matrix-Tree Theorem. Int. Math. Res. Notices 2002, No. 27, 1397-1426. Preprint (version: February 2002) (gzipped postscript, 233 K), (First Version: September 2001), also available as math.CO/0109104. Journal Version

(with J. E. Andersen) Involutions on Moduli Spaces and Refinements of the Verlinde Formula. Math. Annalen 314 (1999) 291-326. Preprint (version: November 2, 1998) (gzipped postscript, 127 K) (First Version: October 22, 1997), also available as alg-geom/9710031. Journal Version

(with H. Wenzl) Integral modular categories and Integrality of Quantum Invariants at Roots of Unity of Prime Order. J. reine angew. Math. (Crelle's Journal) 505 (1998), 209-235. Preprint (version: May 29, 1998) (gzipped postscript, 114 K) (First version: March 7, 1997).

(with N. Habegger) The Kontsevich integral and Milnor's invariants. Topology 39 (2000) 1253-1289. Preprint (version: April 7, 1999) (gzipped postscript, 140 K) (First version: April 2, 1997). Journal version

An element of infinite order in TQFT-representations of mapping class groups. Contemp. Math. 233 (1999) 137-139. (Proceedings of the Conference on Low Dimensional Topology in Funchal, Madeira, 1998.) Preprint May 1998 (Postscript, 71 K)

(with J. D. Roberts) A simple proof of integrality of quantum invariants at prime roots of unity. Math. Proc. Cam. Phil. Soc. 121 (1997) 443-454.

The spin refined Kauffman bracket skein module of $S^1\times S^2$ and lens spaces. Manuscripta Math. 91 (1996) 495-509.

(with C. Blanchet) Topological quantum field theories for surfaces with spin structure. Duke Math. J. 82 (1996) 229-267. Journal version

Spin TQFT and the Birman-Craggs homomorphisms. In: Proceedings of Third Gokova Geometry-Topology Conference (Turkish J. of Math. 19 (1995) 189-199).

On representations of spin mapping class groups arising in Spin TQFT. In: Geometry and Physics (J. Andersen, J. Dupont, H. Pedersen, A. Swann, Eds.) (Proceedings Conf. Aarhus 95) Marcel Dekker (1996)

Introduction to Spin TQFT. In: Geometric Topology (W. Kazez, Ed.), Proc. Georgia Int. Topology Conf. 1993, AMS/IP Studies in Advanced Mathematics (1997) Vol. 2 (Part 1) 203-216.

(with J. D. Roberts) On central extensions of mapping class groups. Math. Ann. 302, 131-150 (1995).

(with C. Blanchet, N. Habegger, P. Vogel) Topological quantum field theories derived from the Kauffman bracket. Topology 34 (1995) 883-927.

(with C. P. Rourke) Model categories and topological quantum field theories. In: Proceedings of Second Gokova Geometry-Topology Conference (Turkish J. of Math. 18 (1994) 70-80).

(with P. Vogel) Verlinde formulae for surfaces with spin structure. Contemp. Math. 164 (1994) 119-137.

(with P. Vogel) 3-valent graphs and the Kauffman bracket. Pacific J. Math. 164 (1994) 361-381.

(with C. Blanchet, N. Habegger, P. Vogel) Remarks on the three-manifold invariants $\theta _p$. In: Operator Algebras, Mathematical Physics, and Low Dimensional Topology (R. Herman, B. Tanbay, Eds.) A. K. Peters Research Notes in Mathematics Vol 5 (1993), 39-59.

(with C. Blanchet, N. Habegger, P. Vogel) Three-manifold invariants derived from the Kauffman bracket. Topology 31 (1992), 685-699.

On the cohomology of the classifying space of the gauge group over some 4-complexes. Bull. Soc. Math. France 119 (1991) 1-31 (1991).

Sur la cohomologie du classifiant du groupe de jauge sur certains 4-complexes. C. R. Acad. Sci. Paris 310, Série I, 115-118 (1990).

Sur l'algèbre de cohomologie entière du classifiant du groupe de jauge. C. R. Acad. Sci. Paris 307, Série I, 339-342 (1988).

Organismes de rattachement

• Equipe Topologie et géométrie algébriques de l'Institut de Mathématiques de Jussieu