{"id":19,"date":"2012-09-05T11:22:25","date_gmt":"2012-09-05T15:22:25","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=19"},"modified":"2026-03-19T08:17:59","modified_gmt":"2026-03-19T12:17:59","slug":"publications","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/kknudson\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\r\n
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Publications<\/h1>\n\n\n\n

Homology of Linear Groups and K-theory<\/h3>\n\n\n\n

The homology of \\( SL_2(F[t,t^{-1}]) \\)<\/em>, J. Algebra 180<\/strong> (1996), 87-101.<\/p>\n\n\n\n\n\n

The homology of special linear groups over polynomial rings<\/em>, Ann. Sci. Ecole Norm. Sup. (4) 30<\/strong> (1997), 385-416.<\/p>\n\n\n\n\n\n

Congruence subgroups and twisted cohomology of \\( SL_n(F[t]) \\)<\/em>, J. Algebra 207<\/strong> (1998), 695-721.<\/p>\n\n\n\n\n\n

Integral homology of \\( PGL_2 \\) over elliptic curves<\/em>, Algebraic K-theory, Seattle, WA, 1997, Proc. Symp. Pure Math. 67<\/strong> (1999), 175-180.<\/p>\n\n\n\n\n\n

On the K-theory of elliptic curves<\/em>, J. reine angew. Math. 507<\/strong> (1999), 81-91.<\/p>\n\n\n\n\n\n

Unstable homotopy invariance and the homology of \\( SL_2(Z[t]) \\)<\/em>, J. Pure Appl. Algebra. 148<\/strong> (2000), 255–266.<\/p>\n\n\n\n\n\n

Congruence subgroups and twisted cohomology of \\( SL_n(F[t]) \\) II. Finite fields and number fields<\/em>, Comm. Alg. 29<\/strong> (2001), 5465–5475.<\/p>\n\n\n\n\n\n

Unstable homotopy invariance for finite fields<\/em>, Fund. Math. 175<\/strong> (2002), 155–162.<\/p>\n\n\n\n\n\n

(with M. Walker) Homology of linear groups via cycles in \\( BG \\times X \\)<\/em>, J. Pure Appl. Algebra 192<\/strong> (2004), 187–202.<\/p>\n\n\n\n\n\n

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

Relative Completions<\/h3>\n\n\n\n

Relative completions of linear groups over \\( Z[t] \\) and \\( Z[t,t^{-1}] \\)<\/em><\/a>, Trans. Amer. Math. Soc. 352<\/strong> (2000), 2205–2216.<\/p>\n\n\n\n\n\n

Correction to “Relative Completions…”<\/em>, Trans. Amer. Math. Soc. 353<\/strong> (2001), 3833–3834.<\/p>\n\n\n\n\n\n

Relative completions and the cohomology of linear groups over local rings<\/em>, J. London Math. Soc. (2), 65<\/strong> (2002), 183–203.<\/p>\n\n\n\n\n\n

Relative completions of linear groups over coordinate rings of curves<\/em>, Comm. Alg. 35<\/strong> (2007), 3904–3908.<\/p>\n\n\n\n\n\n

Relative completions of linear groups<\/em> L’Enseign. Math., 54<\/strong> (2008), 119–121.<\/p>\n\n\n\n

Computational Topology and Discrete Morse Theory<\/h3>\n\n\n\n

Approximate triangulations of Grassmann manifolds<\/em>, Algorithms\u00a013<\/strong> (7) (2020), art. 172. (link<\/a>)<\/p>\n\n\n\n\n\n

(with L. Johnson)\u00a0Min-max theory for cell complexes<\/em>, Algebra Colloq.\u00a027<\/strong> (2020), 447–454.<\/p>\n\n\n\n\n\n

(with B. Wang) Discrete Stratified Morse Theory: A User’s Guide<\/em>, Proceedings of the 34th Symposium on Computational Geometry (2018). (link<\/a>)<\/p>\n\n\n\n\n\n

(with H. King and N. Mramor) Generating discrete Morse functions from point data<\/em>, Experimental Math. 14<\/strong> (2005), 435–444.<\/p>\n\n\n\n\n\n

(with H. King and N. Mramor) Birth and death in discrete Morse theory<\/em>, J. Symbolic Comput. 78<\/strong> (2017), 41-60.<\/p>\n\n\n\n\n\n

A refinement of multi-dimensional persistent homology<\/em>, Homology, Homotopy Appl., 10<\/strong> (2008), 259–281.<\/p>\n\n\n\n\n\n

(with K. Brown) Nonlinear statistics of human speech data<\/em>, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 19<\/strong> (2009), 2307-2319.<\/p>\n\n\n\n\n\n

(with K. Brown)Persistent homology for speech recognition<\/em>, preprint (2008).<\/p>\n\n\n\n\n\n

Persistent homology as discrete Morse theory<\/em>, in preparation.<\/p>\n\n\n\n

Miscellaneous Topology Papers<\/h3>\n\n\n\n

On the kernel of the Gassner representation<\/em>, Arch. Math. (Basel), 85<\/strong> (2005), 108–117.<\/p>\n\n\n\n\n\n

The homology of invariant group chains<\/em>, J. Algebra 298<\/strong> (2006), 15–33.<\/p>\n\n\n\n\n\n

Invariant chains and the homology of quotient spaces<\/em>, preprint(2004).<\/p>\n\n\n\n

Books<\/h3>\n\n\n\n

Homology of Linear Groups<\/em>, Progress in Mathematics, vol. 193, Birkhauser Boston, 2000.<\/p>\n\n\n\n\n\n

Morse Theory: Smooth and Discrete<\/em>, World Scientific, Singapore, 2015.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":11,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":11,"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":505,"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/pages\/19\/revisions\/505"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/kknudson\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}