Research Interests

Research Interests

$\bullet$ Algebraic $K$-and $L$-theory.
$\bullet$ Geometric group theory.
$\bullet$ Conformal nets, topological quantum field theory.

Selected Publications

Selected Publications of Arthur Bartels

$\bullet$ A. Bartels, C. L. Douglas, and A. Henriques. Conformal nets {II}: Conformal blocks. Comm. Math. Phys., 354(1):393–458, 2017.

$\bullet$ A. Bartels. Coarse flow spaces for relatively hyperbolic groups. Compos. Math., 153(4):745–779, 2017.

$\bullet$ A. Bartels, C. L. Douglas, and A. Henriques. Conformal nets I: Coordinate-free nets. Int. Math. Res. Not. IMRN, 2015(13):4975–5052, 2015.

$\bullet$ A. Bartels, W. Lück, H. Reich, and H. Rüping. K- and L-theory of group rings over $GL_n({\bf Z})$. Publ. Math. Inst. Hautes \'Etudes Sci., 119(1):97–125, 2014.

$\bullet$ A. Bartels, F. T. Farrell, and W. Lück. The Farrell- Jones conjecture for cocompact lattices in virtually connected Lie groups. J. Amer. Math. Soc., 27(2):339–388, 2014.

$\bullet$ A. Bartels and W. Lück. The Borel conjecture for hyperbolic and ${\rm CAT}(0)$-groups. Ann. of Math. (2), 175(2):631–689, 2012.

$\bullet$ A. Bartels, W. Lück, and S. Weinberger. On hyperbolic groups with spheres as boundary. J. Differential Geom., 86(1):1–16, 2010.

$\bullet$ A. Bartels, W. Lück, and H. Reich. The $K$-theoretic Farrell- Jones conjecture for hyperbolic groups. Invent. Math., 172(1):29–70, 2008.

$\bullet$ A. Bartels, F. T. Farrell, L. Jones, and H. Reich. On the isomorphism conjecture in algebraic $K$-theory. Topology, 43(1):157–213, 2004.

$\bullet$ A. Bartels. Squeezing and higher algebraic $K$-theory. $K$-Theory, 28(1):19–37, 2003.

Current Publications

$\bullet $ A. Bartels and W. Lueck. Vanishing of Nil-terms and negative K-theory for additive categories. arXiv e-prints, February 2020. arXiv:2002.03412v1.

$\bullet $ A. Bartels, C. L. Douglas, and A. Henriques. Conformal nets V: dualizability. arXiv e-prints, May 2019. arXiv:1905.03393.

$\bullet $ A. Bartels, C. L. Douglas, and A. Henriques. Fusion of defects. Memoirs of the American Mathematical Society, 258(1237):vii+100, March 2019. doi:10.1090/memo/1237.

$\bullet $ A. Bartels and M. Bestvina. The Farrell-Jones conjecture for mapping class groups. Inventiones Mathematicae, 215(2):651–712, January 2019. URL: https://doi.org/10.1007/s00222-018-0834-9, doi:10.1007/s00222-018-0834-9.