Non-Zero Degree Maps Between
<Emphasis Type="Italic">2n</Emphasis>-Manifolds |
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Authors: | Email author" target="_blank">Hai?Bao?DuanEmail author Shi?Cheng?Wang |
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Institution: | (1) Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Science, Beijing, 100080, P. R. China;(2) LMAM, Department of Mathematics, Peking University, Beijing, 100871, P. R. China |
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Abstract: | Abstract
Thom–Pontrjagin constructions are used to give a
computable necessary and sufficient condition for a homomorphism ϕ
: H
n
(L;Z) → H
n
(M;Z) to be realized by a map
f : M → L of degree k for closed (n − 1)-connected 2n-manifolds M and L,
n > 1. A corollary is that
each (n − 1)-connected
2n-manifold admits selfmaps
of degree larger than 1, n
> 1.
In the most interesting case of dimension 4, with the
additional surgery arguments we give a necessary and sufficient
condition for the existence of a degree k map from a closed orientable
4-manifold M to a closed
simply connected 4-manifold L
in terms of their intersection forms; in particular, there is a
map f :
M → L of degree 1 if and only if the
intersection form of L is
isomorphic to a direct summand of that of
M.
Both authors are supported by MSTC, NSFC. The
comments of F. Ding, J. Z. Pan, Y. Su and the referee enhance
the quality of the paper |
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Keywords: | 2n-manifolds Non-zero degree maps |
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