Jerome Levine's electronically available papers

Jumps of the Atiyah-Patodi-Singer eta invariant
(with M. Farber) Mathematische Zeitschrift. 223 (1996), pp. 197-246.

Deformations of representations and cohomology
Preprint (1996).

Finite-type invariants of 3-manifolds.II
(with S. Garoufalidis) Mathematische Annalen. 306 (1996), pp. 691-718.

Finite-type invariants of 3-manifolds, IV: Comparison of definitions
(with S. Garoufalidis). Proceedings of Cambridge Philosophical Society 122(2) (1997), pp.291-300.

Finite-type invariants, blinks and the mapping class group
(with S. Garoufalidis). J. Diff. Geometry, 47(2) (1997)

Morse theory of harmonic forms
(with M. Farber and G. Katz), Topology, 37(3) (1998), pp. 469-83.

Finite-type 3-manifold invariants and the structure of the Torelli group
(with S. Garoufalidis), Inventiones Math., 131(3) (1998), pp. 541-94.

The Conway polynomial of an algebraically split link.
Proceedings of KNOTS 96, ed. S. Suzuki, World Scientific Publishing Co. 1997, pp. 23-29

A factorization of the Conway polynomial.
Comment. Math. Helveticii 74 (1999), pp. 1-27

A survey of applications of surgery to knot and link theory.
(with Kent Orr), Surveys on surgery theory, vol. 1, ed. S. Cappell, A. Ranicki, J. Rosenberg, Annals of Math. Studies 145, Princeton U. Press (2000)

Pure braids, a new subgroup of the mapping class group and finite-type invariants.
Tel Aviv Topology Conference: Rothenberg Festschrift, ed. M. Farber, W. Luck, S. Weinberger, Contemporary Mathematics 231 (1999).

Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism.
(with S. Garoufalidis) Graphs and Patterns in Mathematics and Theoretical Physics, Proceedings Symp. Pure Math. 73 (2005) pp. 173--205..

Homology surgery and invariants of three-manifolds.
(with S. Garoufalidis) Geometry and Topology 5 (2001), pp. 551--578.

Analytic invariants of boundary links.
(with S. Garoufalidis) Journal of Knot Theory and its Ramifications 11 (2002), pp. 283--294.

Homology cylinders: an enlargement of the mapping class group.
Algebraic and Geometric Topology 1 (2001), pp. 243-270.

Concordance and 1-loop clovers.
(with S. Garoufalidis) Algebraic and Geometric Topology 1 (2001), pp. 687-697.

Addendum and correction to "Homology cylinders: an enlargement of the mapping class group".
Algebraic and Geometric Topology 2 (2002), pp. 1197-1204.

Concordance of boundary links
Journal of Knot Theory and its Applications 16 (2007), no. 9, 1111--1120.

The Lagrangian filtration of the mapping class group and finite-type invariants of homology spheres
Mathematical proceedings of the Cambridge Philosophical Society 141 (2006), no. 2, 303--315.

Labeled binary planar trees and quasi-Lie algebras
Algebra. Geom. Topol. 6 (2006), 935--948.

Here are some old papers. Most of them are accessed from JSTOR (for which you must be connected through an institution which has a subscription).

A classification of differentiable knots
Annals of Math. 82 (1963), pp.15-50.

A characterization of knot polynomials
Topology 4 (1965), 135-41.

Finding a boundary for an open manifold
(with G. Livesay and W. Browder), Amer. J. Math. 87 (1965), 1017- 28.

Polynomial invariants of knots of codimension two
Annals of Math., Vol. 84 (1966), 537-54.

A method for generating link polynomials
Amer. J. Math., Vol. 89 (1967), 69-84.

Knot modules
Trans. AMS 229 (1977), 1-50.

Surgery on links and the µ-invariants
Topology, 26 (1987), 45-61.

An approach to homotopy classification of classical links
Trans. A.M.S., 306 (1988), 361-87.