Research

• algebraic K-theory, Waldhausen K-theory and pseudoisotopy theory
• geometric group theory
• large scale geometry and topology
• low dimensional topology, knots and links
• metric geometry
• moduli spaces and gauge theory
• representation theory
• surgery theory of manifolds

Publications:

• Dragomir, George; Nicas, Andrew. The Quasi-hyperbolicity Constant of a Metric Space. Math. Inequal. Appl. 24 (2021), no.4, 1041-1064. Preprint version: arXiv 1908.04440


• Nicas, Andrew; Rosenthal, David. Finitely F-amenable actions and Decomposition Complexity of Groups. Groups Geom. Dyn. 14 (2020), no.3, 765-790. Preprint version: arXiv 1804.09207


• Boden, Hans; Nicas, Andrew. Virtual and welded periods of classical knots. Breadth in Contemporary Topology, 29-42. Proc. Sympos. Pure Math., 102, Amer. Math. Soc., Providence, RI, 2019. Preprint version: arXiv 1711.04051


• Dragomir, George; Nicas, Andrew. Metric transforms yielding Gromov hyperbolic spaces. Geometriae Dedicata 200 (2019), no.1, 331-350. Preprint version: arXiv 1710.05078


• Boden, Hans; Nicas, Andrew; White, Lindsay. Alexander invariants of periodic virtual knots. Dissertationes Mathematicae 530 (2018), 59 pp. Preprint version: arXiv 1706.02671


• Kasprowski, Daniel; Nicas, Andrew; Rosenthal, David. Regular Finite Decomposition Complexity. Journal of Topology and Analysis 11 (2019), no.3, 691-791. Preprint version: arXiv 1608.04516


• Nicas, Andrew; Rosenthal, David. Hyperbolic Dimension and Decomposition Complexity. Topological Methods in Group Theory, 146-167, London Mathematical Society Lecture Notes Series., 451, Cambridge Univ. Press, Cambridge, 2018. Preprint version: arXiv 1509.06437.


• Boden, Hans U.; Gaudreau, Anne Isabel; Harper, Eric; Nicas, Andrew J.; White, Lindsay. Virtual knot groups and almost classical knots. Fund. Math. 238 (2017), no. 2, 101-142. MR3640614   Preprint version: arXiv 1506.01726.


• Boden, Hans U.; Dies, Emily; Gaudreau, Anne Isabel; Gerlings, Adam; Harper, Eric; Nicas, Andrew J. Alexander invariants for virtual knots. J. Knot Theory Ramifications 24 (2015), no. 3, 1550009, 62 pp. MR3342135


• Dies, Emily; Nicas, Andrew. The center of the virtual braid group is trivial. J. Knot Theory Ramifications 23 (2014), no. 8, 1450042, 6 pp. MR3261954


• Nicas, Andrew; Rosenthal, David. On the asymptotic dimension of the dual group of a locally compact abelian group. Topology Appl. 160 (2013), no. 5, 682-684. MR3022735


• Cappadocia, Chris; Nicas, Andrew. Moduli of triangles in the Heisenberg group. Geom. Dedicata 161 (2012), 189-219. MR2994038


• Nicas, Andrew; Rosenthal, David. Coarse structures on groups. Topology Appl. 159 (2012), no. 14, 3215-3228. MR2948279


• Klein, Tom; Nicas, Andrew. The horofunction boundary of the Heisenberg group: the Carnot-Carathéodory metric. Conform. Geom. Dyn. 14 (2010), 269-295. MR2738530


• Klein, Tom; Nicas, Andrew. The horofunction boundary of the Heisenberg group. Pacific J. Math. 242 (2009), no. 2, 299-310. MR2546714


• Nicas, Andrew; Rosenthal, David. Finite Z/2Z-CW complexes which are not homotopically stratified by orbit type. Proc. Amer. Math. Soc. 137 (2009), no. 1, 381-384. MR2439463


• Nicas, Andrew; Rosenthal, David. Hochschild homology relative to a family of groups. Algebr. Geom. Topol. 8 (2008), no. 2, 693-728. MR2443093


• Fernandes, Praphat; Nicas, Andrew. Classification of di-embeddings of the n-cube into Rⁿ. Homology, Homotopy Appl. 9 (2007), no. 1, 213-220. MR2280293


• Nicas, Andrew. Combinatorial identities in the theory of SU(n) Casson invariants of knots. Pure Appl. Math. Q. 2 (2006), no. 3, part 1, 795-816. MR2252118


• Nicas, Andrew. Trace and duality in symmetric monoidal categories. K-Theory 35 (2005), no. 3-4, 273-339 (2006). MR2240236


• Geoghegan, Ross; Nicas, Andrew; Schütz, Dirk. Obstructions to homotopy invariance in parametrized fixed point theory. Geometry and topology: Aarhus (1998), 157-175, Contemp. Math., 258, Amer. Math. Soc., Providence, RI, 2000. MR1778102


• Boden, Hans U.; Nicas, Andrew. Universal formulae for SU(n) Casson invariants of knots. Trans. Amer. Math. Soc. 352 (2000), no. 7, 3149-3187. MR1695018


• Geoghegan, Ross; Nicas, Andrew. Fixed point theory and the K-theoretic trace. Nielsen theory and Reidemeister torsion (Warsaw, 1996), 137-149, Banach Center Publ., 49, Polish Acad. Sci., Warsaw, 1999. MR1734728


• Geoghegan, Ross; Nicas, Andrew. A Hochschild homology Euler characteristic for circle actions. K-Theory 18 (1999), no. 2, 99-135. MR1711720


• Geoghegan, Ross; Nicas, Andrew; Oprea, John. Higher Lefschetz traces and spherical Euler characteristics. Trans. Amer. Math. Soc. 348 (1996), no. 5, 2039-2062. MR1351489


• Geoghegan, Ross; Nicas, Andrew. Homotopy periodicity and coherence. Proc. Amer. Math. Soc. 124 (1996), no. 9, 2889-2895. MR1346975


• Geoghegan, Ross; Nicas, Andrew. Higher Euler characteristics. I. Enseign. Math. (2) 41 (1995), no. 1-2, 3-62. MR1341940


• Geoghegan, Ross; Nicas, Andrew. Trace and torsion in the theory of flows. Topology 33 (1994), no. 4, 683-719. MR1293306


• Geoghegan, Ross; Nicas, Andrew. The first order Euler characteristic. The Hilton Symposium 1993 (Montreal, PQ), 37-59, CRM Proc. Lecture Notes, 6, Amer. Math. Soc., Providence, RI, 1994. MR1290583


• Geoghegan, Ross; Nicas, Andrew. Parametrized Lefschetz-Nielsen fixed point theory and Hochschild homology traces. Amer. J. Math. 116 (1994), no. 2, 397-446. MR1269610


• Frohman, Charles; Nicas, Andrew. An intersection homology invariant for knots in a rational homology 3-sphere. Topology 33 (1994), no. 1, 123-158. MR1259519


• Geoghegan, Ross; Nicas, Andrew. Lefschetz trace formulae, zeta functions and torsion in dynamics. Nielsen theory and dynamical systems (South Hadley, MA, 1992), 141-157, Contemp. Math., 152, Amer. Math. Soc., Providence, RI, 1993. MR1243472


• Frohman, Charles; Nicas, Andrew. The Alexander polynomial via topological quantum field theory. Differential geometry, global analysis, and topology (Halifax, NS, 1990), 27-40, CMS Conf. Proc., 12, Amer. Math. Soc., Providence, RI, 1991. MR1158467


• Nicas, A. J.; Stark, C. W. Deformations of groups of gauge transformations. J. Funct. Anal. 101 (1991), no. 2, 408-441. MR1136943


• Nicas, Andrew J. Classifying pairs of Lagrangians in a Hermitian vector space. Topology Appl. 42 (1991), no. 1, 71-81. MR1135782


• Boyer, S.; Nicas, A. Varieties of group representations and Casson's invariant for rational homology 3-spheres. Trans. Amer. Math. Soc. 322 (1990), no. 2, 507-522. MR0972701


• Nicas, Andrew J. Mixed Hodge structure in cyclic homology and algebraic K-theory. I. K-Theory 1 (1987), no. 5, 437-456. MR0934450


• Nicas, A. J.; Stark, C. W. Whitehead groups of certain hyperbolic manifolds. II. Combinatorial group theory and topology (Alta, Utah, 1984), 415-431, Ann. of Math. Stud., 111, Princeton Univ. Press, Princeton, NJ, 1987. MR0895625


• Nicas, Andrew J. Frobenius induction for higher Whitehead groups. Canad. J. Math. 39 (1987), no. 1, 222-238. MR0889112


• Nicas, Andrew J. Mixed Hodge structure in algebraic K-theory and cyclic homology. C. R. Math. Rep. Acad. Sci. Canada 8 (1986), no. 5, 313-315. MR0859433


• Nicas, Andrew J. An infinite family of non-Haken hyperbolic 3-manifolds with vanishing Whitehead groups. Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 2, 239-246. MR0817665


• Nicas, A. J.; Stark, C. W. K-theory and surgery of codimension-two torus actions on aspherical manifolds. J. London Math. Soc. (2) 31 (1985), no. 1, 173-183. MR0810574


• Storer, J. A.; Nicas, A. J.; Becker, J. Uniform circuit placement. VLSI: algorithms and architectures (Amalfi, 1984), 255-273, North-Holland, Amsterdam, 1985. MR0803730


• Nicas, Andrew J. On the higher Whitehead groups of a Bieberbach group. Trans. Amer. Math. Soc. 287 (1985), no. 2, 853-859. MR0768746


• Nicas, Andrew J. On Wh₂ of a Bieberbach group. Topology 23 (1984), no. 3, 313-321. MR0770567


• Nicas, A.; Stark, C. Surgery up to homotopy equivalence for nonpositively curved manifolds. Proc. Amer. Math. Soc. 91 (1984), no. 2, 323-325. MR0740195


• Nicas, A. J.; Stark, C. W. Higher Whitehead groups of certain bundles over Seifert manifolds. Proc. Amer. Math. Soc. 91 (1984), no. 1, 1-5. MR0735551


• Nicas, A. J.; Stark, C. W. Whitehead groups of certain hyperbolic manifolds. Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 2, 299-308. MR0735370


• Nicas, Andrew J. On Wh₃ of a Bieberbach group. Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 1, 55-60. MR0727080


• Nicas, Andrew J. Induction theorems for groups of homotopy manifold structures. Mem. Amer. Math. Soc. 39 (1982), no. 267, vi+108 pp. MR0668807

Research Collaborators

• Hans Boden, McMaster University
• Steven Boyer, Université du Québec à Montréal.
• Charlie Frohman, University of Iowa.
• Ross Geoghegan, Binghamton University.
• Daniel Kasprowski, Mathematical Institute of the University of Bonn
• John Oprea, Cleveland State University.
• David Rosenthal, St. John's University.
• Chris Stark, NSF.

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