Welcome to the page describing Eugene Lerman's research


I am interested in contact and symplectic geometry, and Hamiltonian systems.

Papers and monographs:

[21] Lerman, E., Contact toric manifolds, www.arXiv.org/abs/math.SG/0107201

[20] Lerman, E., Shirokova, N., Toric integrable geodesic flows, submitted to Math Research Letters, www.arXiv.org/abs/math.DG/0011139 .

[19] Lerman, E., A convexity theorem for torus actions on contact manifolds Illinois J. Math , to appear, www.arXiv.org/abs/math.SG/0012017

[18] Lerman, E., Contact Cuts, Israel J. Math , 124 (2001), 77--92; www.arXiv.org/abs/math.SG/000204 .

[17] 2001k:53163 Lerman, E.; Tolman, S. Intersection cohomology of $S\sp 1$ symplectic quotients and small resolutions. Duke Math. J. 103 (2000), no. 1, 79--99.

[16] 2001j:53112 Lerman, Eugene; Willett, Christopher, The topological structure of contact and symplectic quotients, Internat. Math. Res. Notices 2001, no. 1, 33--52.

[15] 2000b:37066 Lerman, Eugene; Tokieda, Tadashi, On relative normal modes C. R. Acad. Sci. Paris Sér. I Math. 328 (1999), no. 5, 413--418.

[14] 99j:58077 Lerman, E.; Singer, S.F., Stability and persistence of relative equilibria at singular values of the moment map, Nonlinearity 11 (1998), no. 6, 1637--1649. [original article]
(access may require subscription to Nonlinearity ).
Early version of this paper was posted as dg-ga/9706009 (see below)

[13] 99a:58069 Lerman, Eugene; Meinrenken, Eckhard; Tolman, Sue; Woodward, Chris, Nonabelian convexity by symplectic cuts. Topology 37 (1998), no. 2, 245--259. postscript file

[12] 98i:58085 Bates, L.; Lerman, E., Proper group actions and symplectic stratified spaces. Pacific J. Math. 181 (1997), no. 2, 201--229. [original article]

[11] 98e:58077 Karshon, Yael; Lerman, Eugene, The centralizer of invariant functions and division properties of the moment map. Illinois J. Math. 41 (1997), no. 3, 462--487. 58F05 (57S15 57S25) gzip'ed dvi file

[10] 98d:58074 Guillemin, Victor; Lerman, Eugene; Sternberg, Shlomo, Symplectic fibrations and multiplicity diagrams. Cambridge University Press, Cambridge, 1996. xiv+222 pp. ISBN: 0-521-44323-7 58F06 (17B99 22E45 58F05 81S10)

[9] 98a:57043 Lerman, Eugene; Tolman, Susan, Hamiltonian torus actions on symplectic orbifolds and toric varieties. Trans. Amer. Math. Soc. 349 (1997), no. 10, 4201--4230. [original article]

[8] 97g:57058 Lerman, Eugene, A compact symmetric symplectic non-Kaehler manifold. Math. Res. Lett. 3 (1996), no. 5, 587--590. 57S25 (53C15 57R15 57S15)

[7]97c:32045 Lerman, Eugene; Sjamaar, Reyer, Reductive group actions on Kähler manifolds. Conservative systems and quantum chaos (Waterloo, ON, 1992), 85--92, Fields Inst. Commun., 8, Amer. Math. Soc., Providence, RI, 1996. 32M05 (58F05)

[6] 96f:58062 Lerman, Eugene Symplectic cuts. Math. Res. Lett. 2 (1995), no. 3, 247--258. 58F05 (57S25)
dvi , LaTeX

[5] 95h:58054 Lerman, Eugene; Montgomery, Richard; Sjamaar, Reyer, Examples of singular reduction. Symplectic geometry, 127--155, London Math. Soc. Lecture Note Ser., 192, Cambridge Univ. Press, Cambridge, 1993. 58F05 (58A35)

[4] 92g:58036Sjamaar, Reyer; Lerman, Eugene; Stratified symplectic spaces and reduction. Ann. of Math. (2) 134 (1991), no. 2, 375--422. 58F05 (57R15)

[3] 92f:58058 Guillemin, V.; Lerman, E.; Sternberg, S., On the Kostant multiplicity formula. J. Geom. Phys. 5 (1988), no. 4, 721--750 (1989). 58F05 (22E46 22E60 58F06 58G10)

[2] 90k:58070 Lerman, Eugene, On the centralizer of invariant functions on a Hamiltonian $G$-space. J. Differential Geom. 30 (1989), no. 3, 805--815.

[1] 89k:53033 Lerman, Eugene, How fat is a fat bundle? Lett. Math. Phys. 15 (1988), no. 4, 335--339.


e-prints/:

dg-ga/9706009 [abs, src, ps, other] :

Title: Relative equilibria at singular points of the moment map
Author: Eugene Lerman (University of Illinois at Urbana-Champaign)
Comments: 10 pages, LaTeX2e
Subj-class: Differential Geometry
MSC-class: 58F; 70H
A later version is item [14] above

dg-ga/9608010 [abs, src, ps, other] :

Title: Stability of symmetric tops via one variable calculus
Author: Eugene Lerman
Comments: 10 pages, LaTeX, uses epic and eepic style files
Subj-class: Differential Geometry
MSC-class: 58F


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last changed October 29, 2001