Research: Original Scientific Discoveries
Professionally, I am a pure mathematician working in the Topology of High-dimensional Manifolds (CV/résumé).
Partial funding for research is provided by the National Science Foundation, through a grant of which I am the Principal Investigator (DMS-0904276).
From Fall Semester 2010 through Spring Semester 2012, I serve as the organizer of the Notre Dame Topology Research Seminar.
PUBLICATIONS (original work, refereed by anonymous expert)
Immediately after each publication number on the left, you will find the 2010 Journal Quality Ranking of the Australian Research Council:
A* = one of the best in its field or subfield |
A = very high quality |
B = solid, though not outstanding |
C = does not meet the criteria for the higher tiers |
N/A = ranking not available because the journal is too new
MISC report —
The homotopy type of G/PL and the characteristic variety theorem
(with T. Macko), Oberwolfach Rep., 3(3): 2212–2214, 2006 [ published ]
01:A* Manifolds homotopy equivalent to Pn # Pn
(with J. Brookman and J.F. Davis), Math. Annalen, 338(4): 947–962, 2007 [ published | reviewed ]
02:A On smoothable surgery for 4-manifolds
Algebr. Geom. Topol., 7: 2117–2140, 2007 [ published | reviewed ]
03:B On fibering and splitting of 5-manifolds over the circle
Topology Appl., 156(2): 284–299, 2008 [ published | reviewed ]
04:A Reduction of UNil for finite groups with normal abelian Sylow 2-subgroup
J. Pure Appl. Algebra, 213(3): 279–298, 2009 [ published | reviewed ]
05:B Calculation of UNil for the cyclic group of order two
Forum Math., 22(2): 221–239, 2010 [ published | reviewed ]
06:B Dihedral manifold approximate fibrations over the circle
(with C.B. Hughes), Geom. Dedicata, 148(1): 205–243, 2010 [ published | reviewed ]
MISC announcement —
The Nil-Nil theorem in algebraic K-theory
RIMS Kôkyűroku, 1612: 99–100, 2008 [ published ]
07:A Algebraic K-theory over the infinite dihedral group: an algebraic approach
(with J.F. Davis and A. Ranicki), Algebr. Geom. Topol., 11(4): 2391–2436, 2011 [ published | reviewed ]
PREPRINTS (submitted to editor, under academic peer-review)
‣ Homotopy invariance of 4-manifold decompositions: connected sums
submitted (16 pages @ 16 Dec 2011) [ preprint ]
‣ Topological rigidity and H1-negative involutions on tori
(with F. Connolly and J.F. Davis), submitted (36 pages @ 20 Feb 2012) [ preprint ]
‣ announcement —
Rigidity of pseudo-free group actions on contractible manifolds
submitted (6 pages @ 21 Mar 2012) [ preprint ]
Selection of Open Research Projects (private manuscript)
‣ Topological rigidity and pseudo-free actions on contractible manifolds
(with F. Connolly and J.F. Davis), in final edit (13 pages @ 15 Apr 2012)
‣ On smoothable surgery for 4-manifolds, II: fundamental groups with 2-torsion
(with D. Crowley), suspended (6 pages @ 17 Jul 2011)
‣ Homotopy invariance of 4-manifold decompositions, II: sums along circles
supsended (6 pages @ 29 Nov 2009)
‣ Splitting homotopy equivalences along two-sided submanifolds, I: obstruction theory
(with J. Brookman), suspended (14 pages @ 03 Sep 2009)
‣ Calculation of UNil for certain cyclotomic and quadratic number rings
suspended (17 pages @ 22 Jun 2008)
Remnants of Dissertation (unpublished)
a On cancellation for topological 4-manifolds with infinite fundamental group
updated (15 pages @ 11 Sep 2006) [ manuscript ]
b Self-coverings of RPn # RPn and weak nilpotence of UNil under transfers
updated (15 pages @ 11 Sep 2006) [ manuscript ]