14,622 research outputs found
The theorem of the complement for nested subpfaffian sets
Let R be an o-minimal expansion of the real field, and let
L(R) be the language consisting of all nested Rolle leaves over R. We call a
set nested subpfaffian over R if it is the projection of a boolean combination
of definable sets and nested Rolle leaves over R. Assuming that R admits
analytic cell decomposition, we prove that the complement of a nested
subpfaffian set over R is again a nested subpfaffian set over R. As a
corollary, we obtain that if R admits analytic cell decomposition, then the
pfaffian closure P(R) of R is obtained by adding to R all nested Rolle leaves
over R, a one-stage process, and that P(R) is model complete in the language
L(R).Comment: final version before publicatio
Contact handles, duality, and sutured Floer homology
We give an explicit construction of the Honda--Kazez--Mati\'c gluing maps in
terms of contact handles. We use this to prove a duality result for turning a
sutured manifold cobordism around, and to compute the trace in the sutured
Floer TQFT. We also show that the decorated link cobordism maps on the hat
version of link Floer homology defined by the first author via sutured manifold
cobordisms and by the second author via elementary cobordisms agree.Comment: 86 pages, 54 figures, to appear in Geometry and Topolog
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