9,115 research outputs found
The classification of certain linked -manifolds in -space
We work entirely in the smooth category. An embedding is {\it Brunnian}, if the restriction
of to each component is isotopic to the standard embedding. For each triple
of integers such that , we explicitly construct a
Brunnian embedding such that the following theorem holds.
Theorem: Any Brunnian embedding is isotopic to for some integers such that
. Two embeddings and are
isotopic if and only if , and .
We use Haefliger's classification of embeddings in our proof. The following corollary shows that the relation
between the embeddings and
is not trivial.
Corollary: There exist embeddings and such that the
componentwise embedded connected sum is isotopic to but is
not isotopic to
On Welschinger invariants of symplectic 4-manifolds
We prove the vanishing of many Welschinger invariants of real symplectic
-manifolds. In some particular instances, we also determine their sign and
show that they are divisible by a large power of 2. Those results are a
consequence of several relations among Welschinger invariants obtained by a
real version of symplectic sum formula. In particular, this note contains
proofs of results announced in [BP13].Comment: 26 pages, 9 figures. v3: many details added, previous sections 2 and
3 have been merge
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