Homology of Linear Groups and K-theory

The homology of \( SL_2(F[t,t^{-1}]) \), J. Algebra 180 (1996), 87-101.

The homology of special linear groups over polynomial rings, Ann. Sci. Ecole Norm. Sup. (4) 30 (1997), 385-416.

Congruence subgroups and twisted cohomology of \( SL_n(F[t]) \), J. Algebra 207 (1998), 695-721.

Integral homology of \( PGL_2 \) over elliptic curves, Algebraic K-theory, Seattle, WA, 1997, Proc. Symp. Pure Math. 67 (1999), 175-180.

On the K-theory of elliptic curves, J. reine angew. Math. 507 (1999), 81-91.

Unstable homotopy invariance and the homology of \( SL_2(Z[t]) \), J. Pure Appl. Algebra. 148 (2000), 255–266.

Congruence subgroups and twisted cohomology of \( SL_n(F[t]) \) II. Finite fields and number fields, Comm. Alg. 29 (2001), 5465–5475.

Unstable homotopy invariance for finite fields, Fund. Math. 175 (2002), 155–162.

(with M. Walker) Homology of linear groups via cycles in \( BG \times X \), J. Pure Appl. Algebra 192 (2004), 187–202.

Homology and finiteness properties for \( SL_2(Z[t,t^{-1}]) \), Algebr. Geom. Topol. 8 (2008), 2253–2261.

Relative Completions

Relative completions of linear groups over \( Z[t] \) and \( Z[t,t^{-1}] \), Trans. Amer. Math. Soc. 352 (2000), 2205–2216.

Correction to “Relative Completions…”, Trans. Amer. Math. Soc. 353 (2001), 3833–3834.

Relative completions and the cohomology of linear groups over local rings, J. London Math. Soc. (2), 65 (2002), 183–203.

Relative completions of linear groups over coordinate rings of curves, Comm. Alg. 35 (2007), 3904–3908.

Relative completions of linear groups L’Enseign. Math., 54 (2008), 119–121.

Computational Topology and Discrete Morse Theory

Approximate triangulations of Grassmann manifolds, Algorithms 13 (7) (2020), art. 172. (link)

(with L. Johnson) Min-max theory for cell complexes, Algebra Colloq. 27 (2020), 447–454.

(with B. Wang) Discrete Stratified Morse Theory: A User’s Guide, Proceedings of the 34th Symposium on Computational Geometry (2018). (link)

(with H. King and N. Mramor) Generating discrete Morse functions from point data, Experimental Math. 14 (2005), 435–444.

(with H. King and N. Mramor) Birth and death in discrete Morse theory, J. Symbolic Comput. 78 (2017), 41-60.

A refinement of multi-dimensional persistent homology, Homology, Homotopy Appl., 10 (2008), 259–281.

(with K. Brown) Nonlinear statistics of human speech data, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 19 (2009), 2307-2319.

(with K. Brown)Persistent homology for speech recognition, preprint (2008).

Persistent homology as discrete Morse theory, in preparation.

Miscellaneous Topology Papers

On the kernel of the Gassner representation, Arch. Math. (Basel), 85 (2005), 108–117.

The homology of invariant group chains, J. Algebra 298 (2006), 15–33.

Invariant chains and the homology of quotient spaces, preprint(2004).

Books

Homology of Linear Groups, Progress in Mathematics, vol. 193, Birkhauser Boston, 2000.

Morse Theory: Smooth and Discrete, World Scientific, Singapore, 2015.