[show abstract][hide abstract] ABSTRACT: We provide bar and cobar constructions as functors between some categories of
curved algebras and curved augmented coalgebras over a graded commutative ring.
These functors are adjoint to each other.
[show abstract][hide abstract] ABSTRACT: We calculate the self-Floer cohomology with Z/2 coefficients of some immersed
Lagrangian spheres in the affine symplectic submanifolds of C^3 that are
smoothings of A_N surfaces. The immersed spheres are exact and graded.
Moreover, they satisfy a positivity assumption that allows us to calculate the
Floer cohomology as follows: Given auxiliary data a Morse function on S^2 and a
time-dependent almost complex structure, the Floer cochain complex is the Morse
complex plus two generators for each self-intersection point of the Lagrangian
sphere. The Floer differential is defined by counting combinations of Morse
flow lines and holomorphic strips. Using a Lefschetz fibration allows us to
explicitly calculate all holomorphic strips and describe the Floer
differential. For most of the immersed spheres the Floer differential is zero
[show abstract][hide abstract] ABSTRACT: Main theorem of this paper states that Floer cohomology groups in a Hilbert
space are isomorphic to the cohomological Conley Index. It is also shown that
calculating cohomological Conley Index does not require finite dimensional
approximations of the vector field. Further directions are discussed.
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