The Maslov index

Seminar (Edinburgh, Autumn 2009)

Maslov index I.,II., Teru Thomas, Monday 5th and 12th October, 3PM, JCMB, Room 6301. Lecture notes courtesy of Thomas Köppe.
Novikov additivity of the signature, Wall non-additivity and the Maslov index, Andrew Ranicki, Monday 26th October, 3PM, JCMB, Room 6301.

An introduction to the Maslov index in symplectic topology, Andrew Ranicki and Daniele Sepe, Monday 9th November, 3PM, JCMB, Room 6301.

The Maslov index and representations of finite nilpotent groups, Gwyn Bellamy, Monday, 16th November, 3PM, JCMB, Room 6301.

The multisignature, the Maslov index and the L²-signature, Andrew Ranicki, Friday, 11th December, 2PM, JCMB, Room 6206.

The Maslov index, the signature and bagels, Andrew Ranicki, Tuesday, 22nd December, Göttingen.

References

The Wikipedia article on the Maslov index.

There are 25,000 entries for the Maslov index on Google.

There are 22,500 entries for the Maslov index on Google Scholar.

There are 400 entries for the Maslov index on Mathematical Reviews.

V.I.Arnold, On a characteristic class entering into conditions of quantisation English translation. Functional Analysis and Its Applications 1, 1-14 (1967)

V.I.Arnold, Sturm theorems and symplectic geometry English translation. Functional Analysis and Its Applications 19, 1-10 (1985)

V.I.Arnold and A.B.Givental, Symplectic geometry Translated from 1985 Russian original. in Dynamical Systems IV, Encycl. of Math. Sciences 4, Springer, 1-136 (1990)

M.Atiyah, The logarithm of the Dedekind η-function, Math. Ann. 278, 335--380 (1987)

D.Auroux, Monodromy invariants in symplectic topology IPAM notes (2003)

R.Bott, On the iteration of closed geodesics and the Sturm intersection theory Comm. Pure and Appl. Maths. 9, 171--206 (1956)

U.Bunke On the glueing problem for the η-invariant J. Diff. Geo. 41, 397--448 (1995)

L.Butler The Maslov cocycle, smooth structures and real-analytic complete integrability, http://uk.arxiv.org/abs/0708.3157, to appear in Am. J. Math.

S.Cappell, R.Lee and E.Y.Miller, On the Maslov index, Comm. Pure Appl. Math. 47, 121--186 (1994)

T.Cochran, K.Orr, P.Teichner, Knot concordance, Whitney towers and L²-signatures, Ann. of Maths. 157, 433--519 (2003)

G.Contreras, J.-M. Gambaudo, R. Iturriaga, G. Paternain, The asymptotic Maslov index and its applications, Ergod. Th. & Dynam. Sys. 23, 1415--1443 (2003)

M.de Gosson, On the usefulness of an index due to Leray for studying the intersections of Lagrangian and symplectic path, J. Math. Pures Appl. 91, 598-613 (2009)

J.J.Duistermaat, On the Morse index in variational calculus, Adv. Math. 21, 173--195 (1976)

H.M.Edwards, A generalized Sturm theorem Annals of Maths. 80, 22--57 (1964)

V.Guillemin and S.Sternberg, Symplectic geometry, Chapter IV of Geometric Optics, Math. Surv. and Mon. 14, AMS, 109-202 (1990)

M.Kamgarpur and T.Thomas, Compatible intertwiners for representations of finite nilpotent groups, http://arxiv.org/abs/0909.5670 (2009)

M.Kashiwara and P.Schapira, Appendix to Sheaves on manifolds, Grundlehren der Math. Wiss. 292, Springer (1992)

J.B.Keller, Corrected Bohr-Sommerfeld Quantum Conditions for Nonseparable Systems, Ann. of Physics 4, 180--188 (1958)

R.Kirby and P. Melvin, Dedekind sums, μ-invariants and the signature cocycle, Math. Ann. 299, 231--267 (1994)

P.Kirk and M.Lesch, On the ρ-invariant for manifolds with boundary, Algebraic and Geometric Topology 3, 623--675 (2003}

P.Kirk and M.Lesch, The η-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary, Forum Mathematicum 16, 553--629 (2004)

L.Kramer and K.Tent, A Maslov cocycle for unitary groups, Proc. Lond. Math. Soc. (3) 100, 91-115 (2010)

J.Leray, The meaning of Maslov's asymptotic method: the need of Planck's constant in mathematics Bull. Amer. Math. Soc. (N.S.) 5, 15--27 (1981)

G.Lion and P.Perrin, Extension des représentations de groupes unipotents p-adiques. Calculs d'obstructions,
Noncommutative harmonic analysis and Lie groups (Marseille, 1980), Springer Lecture Notes in Math. 880, 337--356 (1981)

G.Lion and M.Vergne, The Shale-Weil representation and the Maslov index,
Part I of the The Weil representation, Maslov index and Theta series Progress in Mathematics 6, Birkhäuser (1980)

V.P.Maslov, Theory of perturbations and asymptotic methods, French translation of Russian original (1965), Gauthier-Villars (1972)

50th anniversary of research and teaching by V.P.Maslov, Theoretical and Mathematical Physics 155(2):674--677 (2008)

V.P.Maslov, The intertwining of two lifelines (in memoriam of V.I.Arnold), Russian J. Math. Phys. 17 (4), 395--398 (2010)

D.McDuff and D.Salamon, Linear symplectic geometry, Chapter 2 of Introduction to symplectic topology, Oxford (1998)

A.Nemethi, The eta-invariant of variation structures I., Topology and its Applications 67, 95-111 (1995)

W.Neumann, Signature related invariants of manifolds I. Monodromy and γ-invariants, Topology 18, 147--172 (1979)

R.Parimala, R. Preeti and R. Sridharan, Maslov index and a central extension of the symplectic group, K-theory 19, 29--45 (2000)

P.Piccione and D.Tausk, On the geometry of Grassmannians and the symplectic group: the Maslov index and its applications, Notes (2000)

P.Py, Indice de Maslov et theéorème de Novikov-Wall, Bol. Soc. Math. Mexicana (3) 11, 303--331 (2005)

A.Ranicki, The Maslov index and the Wall signature non-additivity invariant (Unpublished 1997 paper)

C.Sturm, Sur les equations differentielles lineaires du second ordre, J. de Liouville (subsequently J. de Mathematiques Pures et Appliquees) 1, 106--186 (1836)

T.Thomas, The Maslov index as a quadratic space, Math. Res. Lett. 13, 985--999 (2006)

C.Viterbo, A new obstruction to embedding Lagrangian tori. Invent. Math. 100, 301--320 (1990)

C.T.C.Wall, Non-additivity of the signature, Invent. Math. 7, 269--274 (1969)