Home Page of Ross Geoghegan

Department of Mathematical Sciences

State University of New York at Binghamton (Binghamton University)

Binghamton, NY 13902-6000 USA

The State University of New York, University Center at Binghamton, or SUNY-Binghamton for short, is also known as Binghamton University. It is one of the four doctoral granting units of SUNY, the others being at Stony Brook, Albany and Buffalo.

Phone numbers:

(607) 777-2399 (my office)

(607) 777-2147 (department office)

(607) 777-2450 (fax: put my name at top of page)

E-mail:

Office:

Curriculum Vitae and List of Publications

BOOK: "TOPOLOGICAL METHODS IN GROUP THEORY":

BOOK: "THE ART OF PROOF":

RESEARCH INTERESTS:

My primary field of expertise is topology. Within that large area I am particularly interested in the interplay between group theory and geometry/topology. Names of subfields create artificial boundaries in mathematics and I dislike them. But, with that disclaimer, my interests have led me in recent years to work in: geometric and homological group theory, fixed point theory, and certain parts of dynamical systems. Some of the questions motivating this work are algebraic, involving the algebraic K-theory of rings associated with the fundamental group; this is how I got interested in Nielsen fixed point theory, particularly parametrized versions of that theory. Other questions are about how an action by a discrete group on a non-positively curved space can lead to group theoretic information. I'm also interested in understanding the algebraic topology invariants of a group which come from studying the "end" of the universal cover of a suitable classifying (aka K(G,1)) space. There's a vein of information here that has not been mined. This is one of the themes of the above-mentioned book.

RECENT RESEARCH PAPERS

1. Geometric group theory

• R. Bieri and R. Geoghegan, Limit sets for modules over groups on CAT(0) spaces -- from the Euclidean to the hyperbolic preprint June 2013 pdf

• C.Guilbault and R. Geoghegan, Topological properties of spaces admitting free group actions J. Topology 5 (2) 2012, 249-275

• R. Bieri and R. Geoghegan, Sigma Invariants of Direct Products of Groups Groups, Geometry and Dynamics, 4 (2010), 251-261.

• R. Bieri, R. Geoghegan and D. Kochloukova, The Sigma Invariants of Thompson's Group F Groups, Geometry and Dynamics, 4 (2010), 263-273.

• M. Farber, R. Geoghegan and D. Schütz Closed 1-forms in Topology and Geometric Group Theory (Russian) Uspekhi Mat. Nauk 65 (2010), no. 1(391), 145--176; translation in Russian Math. Surveys 65 (2010), no. 1, 143--172.

• R. Geoghegan, The fundamental group at infinity, In “Guido’s Book of Conjectures”(Indira Chatterji, ed.). Monographie de L'Enseignement Mathématique 40 (2008) 97-99.

• R. Geoghegan and F. Guzmán, Associativity and Thompson's Group, Contemporary Mathematics, 394 (2006) 113-135. Postscript file(438KB)

• R. Geoghegan and P. Ontaneda, Boundaries of proper CAT(0) spaces, Topology, 46 (2007) 129-137.

• R. Bieri and R. Geoghegan, Connectivity properties of group actions on non-positively curved spaces, Memoirs of the American Mathematical Society, Volume 161 (Number 765) 2003. (xii + 83 pages), Postscript file(965KB), dvi file(302KB).

• R. Bieri and R. Geoghegan, Topological properties of SL_2 actions on the hyperbolic plane, Geometriae Dedicata 99 (2003) 137-166. Postscript file (578KB), dvi file (125KB).



• R. Bieri and R. Geoghegan, Controlled topology and group actions, in Groups, Combinatorial and Arithmetic Aspects, T. Muller (ed.) London Math. Soc. Lecture Notes Series, vol 311, 2004, Postscript file (472KB) , dvi file (82KB).

• R. Geoghegan, M. L. Mihalik, M. Sapir and D. Wise, Ascending HNN extensions of finitely generated free groups are Hopfian,, Postscript file (194KB) Bull. London Math. Soc.(2001), 33:292-298.

• R. Bieri and R. Geoghegan, Kernels of Actions on Non-Positively Curved Spaces, in Geometry and Cohomology in Group Theory, Peter H. Kropholler, Graham A. Niblo, Ralph Stöhr (ed.) London Math. Soc. Lecture Notes Series, vol. 252, 1998, pp. 24-38.
  

• R. Geoghegan and M.L. Mihalik, The Fundamental Group at Infinity, Topology 35 (1996), 655-669.

2. Fixed point theory and dynamics

• R. Geoghegan, Nielsen fixed point theory, a chapter of "Handbook of Geometric Topology" edited by R. J. Daverman and R. B. Sher, Elsevier, 2003 pp. 499-521. PostScript file (715KB) dvi file (107KB).

• R. Geoghegan, A. Nicas and D. Schütz, Obstructions to homotopy invariance in parametrized fixed point theory, Geometry and Topology: Aarhus, Contemp. Math. Vol 258, (2000) 351--369. PostScript file (415KB). dvi file (115KB).

• R. Geoghegan and A. Nicas, A Hochschild homology Euler characteristic for circle actions, PostScript file (498KB), K-Theory 18 (1999) 99-135.

• R. Geoghegan and A. Nicas, Fixed point theory and the K-theoretic trace, "Nielsen Theory and Reidemeister Torsion", Jerzy Jezierski ed., Banach Center Publications, Warsaw, 1999, pp. 137-149 PostScript file (559KB), dvi file (65KB). 1999.
  

• R. Geoghegan, A. Nicas and J. Oprea, Higher Lefschetz traces and spherical Euler characteristics, Trans. Amer. Math. Soc. 348 (1996), 2039-2062.
  

• R. Geoghegan and A. Nicas, Higher Euler Characteristics (I), L'Enseignement Mathématique, 41(1995) 3-62.
  

• R. Geoghegan and A. Nicas, Trace and torsion in the theory of flows, Topology 33 (1994), 683-719.
  

• R. Geoghegan and A. Nicas, Parametrized Lefschetz-Nielsen fixed point theory and Hochschild homology traces, Amer. J. Math. 116 (1994), 397-446.
  

3. Other topology

• R. Geoghegan and A. Nicas, Homotopy periodicity and coherence, Proc. Amer. Math. Soc., 124 (1996), 2889-2895.

4. Applied mathematics

• R. Geoghegan, J. C. Lagarias and R. C. Melville, Threading homotopies and DC operating points in nonlinear circuits, Society for Industrial and Applied Mathematics (SIAM) Journal on Optimization, 9 (1999) 159-178, download information

Link for Math 220