### 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.