Ph.D., 1970, Cornell University
At Binghamton since 1972
Areas of interest: Topology, geometric group theory, fixed point theory, dynamics
Summary of research interests
- Office: LN 2222
- Office hours:
- Ph. D. Students:
Thesis: Controlled Connectivity for Cocompact Isometric Actions on Simplicial Trees
Thesis: Groups of Geometric Dimension 2
Thesis: Filtered ends of pairs of groups
Thesis: Controlled Topology Invariants of Translation Actions
Thesis: Torsion properties of the Novikov complex
Thesis: Finiteness and CAT(0) Properties of Diagram Groups
Thesis: A Polyhedral Transversality Theorem For One-Parameter Fixed Point Theory
Thesis: Fake surfaces, thickenings and cohomology of groups
(Co-advisor Craig Squier)
Thesis: Tilings of the plane, and hyperbolic groups.
Thesis: Minimizing the Number of Fixed Points for Self-Maps of Compact Surfaces
Thesis: Non-Simply Connected Casson Handles
Thesis: The Missing Boundary Problem for Smooth Manifolds of Dimension Greater Than or Equal to Six
Thesis: Ends of Fundamental Groups in Shape and Proper Homotopy
Home Page of Ross Geoghegan
Home Page of Ross Geoghegan
Ross Geoghegan, Professor of Mathematics
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
(607) 777-2377 (my office)
(607) 777-2147 (department office)
(607) 777-2450 (fax: put my name at top of page)
"TOPOLOGICAL METHODS IN GROUP THEORY":
book "Topological Methods in Group Theory" is Volume 243 of the series
Graduate Texts in Mathematics (Springer 2008). For the book's home page click
To order from Springer click here.
To see a table of Contents, click here.
Curriculum Vitae and List of Publications
"THE ART OF PROOF": This textbook, written
with Matthias Beck, is published in the Springer series Undergraduate
Texts in Mathematics. It is written for a one-semester course for
undergraduates who are learning to read, write and do mathematics at a
professioinal level. Usually, the course is taken after calculus and
before analysis and abstract algebra. For the book's home page click
Topology, geometric group theory, fixed point theory, dynamics.
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
(for full list click Curriculum Vitae):
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,
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),
- 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),
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,
- 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 461
``Classification of Surfaces'' by John Stillwell
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