A generalisation of the Morse inequalities

In this paper we construct a family of variational families for a Legendrian embedding, into the 1-jet bundle of a closed manifold, that can be obtained from the zero section through Legendrian embeddings, by discretising the action functional. We compute the second variation of a generating function obtained as above at a nondegenerate critical point and prove a formula relating the signature of the second variation to the Maslov index as the mesh goes to zero. We use this to prove a generalisation of the Morse inequalities thus refining a theorem of Chekanov.


ONSIPER, H (Cambridge University Press (CUP), 1992-03-01)
Given a smooth projective surface X over an algebraically closed field k and a modulus (an effective divisor) m on X, one defines the idle class group Cm(X) of X with modulus m (see 1, chapter III, section 4). The corresponding generalized Albanese variety Gum and the generalized Albanese map um:X|m|Gum have the following universal mapping property (2): if :XG is a rational map into a commutative algebraic group which induces a homomorphism Cm(X)G(k) (1, chapter III, proposition 1), then factors uniquely th...
On entire rational maps of real surfaces
Ozan, Yıldıray (The Korean Mathematical Society, 2002-01-01)
In this paper, we define for a component X-0 of a nonsingular compact real algebraic surface X the complex genus of X-0, denoted by g(C)(X-0), and use this to prove the nonexistence of nonzero degree entire rational maps f : X-0 --> Y provided that g(C)(Y) > g(C)(X-0), analogously to the topological category. We construct connected real surfaces of arbitrary topological genus with zero complex genus.
On the sequential order continuity of the C(K)-space
Ercan, Z.; Onal, S. (Springer Science and Business Media LLC, 2007-03-01)
As shown in [1], for each compact Hausdorff space K without isolated points, there exists a compact Hausdorff P'-space X but not an F-space such that C(K) is isometrically Riesz isomorphic to a Riesz subspace of C(X). The proof is technical and depends heavily on some representation theorems. In this paper we give a simple and direct proof without any assumptions on isolated points. Some generalizations of these results are mentioned.
A note on Riesz spaces with property-b
Alpay, S.; Altin, B.; Tonyali, C. (Institute of Mathematics, Czech Academy of Sciences, 2006-01-01)
We study an order boundedness property in Riesz spaces and investigate Riesz spaces and Banach lattices enjoying this property.
A generalisation of a theorem of Koldunov with an elementary proof
Ercan, Z (Institute of Mathematics, Czech Academy of Sciences, 1999-01-01)
We generalize a Theorem of Koldunov [2] and prove that a disjointness preserving quasi-linear operator between Resz spaces has the Hammerstein property.
Citation Formats
M. L. Bhupal, “A generalisation of the Morse inequalities,” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, pp. 351–385, 2001, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47447.