The Maslov index
Workshop (AIM, 7-11 April 2014)
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)
- J.Barge and E.Ghys, Cocycles d'Euler et de Maslov, Math. Ann. 294, 235--265 (1992)
- 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)
- J.L.Clerc and B.Orsted
The Maslov index revisited,
Transformation Groups 6, 303-320 (2001)
- 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)
- P.Gilmer and G.Masbaum,
Maslov index, Lagrangians, Mapping Class Groups and TQFT,
Forum Mathematicum 25, 1067-1106 (2011)
- 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, Complement a la theorie d'Arnold de l'indice de Maslov,
Symposia Math. XIV, 33-53 (1974)
- 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.Wahl, Noncommutative Maslov index and η-forms reconsidered, preprint (2016)
- C.T.C.Wall, Non-additivity of the signature,
Invent. Math. 7, 269--274 (1969)