Atlas: On the Euler characteristics of the compact manifold by Sang-Eon Han

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International Conference on Topology and its Applications
August 23-27, 1999
Kanagawa University
Yokohama, Japan

Organizers
Yukinobu Yajima, the chairman, Masami Sakai, the vice-chairman, Yoshihiro Abe, Kazuhiro Sakai, Toshiji Terada, Kenichi Tamano, Akio Kato, Takao Hoshina, Hisao Kato, Kazuhiro Kawamura, Akira Koyama, Tsugunori Nogura

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On the Euler characteristics of the compact manifold
by
Sang-Eon Han
Honam University

Theorem A For the compact manifold X, if X is either of the followings:

X having the locally nilpotent structure has \pi₁(X) torsion-free with all proper subgroups of \pi₁(X) nilpotent

X with the locally nilpotent structure has \pi₁(X) infinite with the maximal condition on normal subgroups of \pi₁(X),

then the Euler characteristics of X is trivial, i.e. \chi(X) = 0.

Theorem B For compact manifolds X, Y, if f : X --> Y is a quasi-nilpotent homology equivalence and X is one of the followings:

X in T_RS,

X is the space satisfying the condition T^* or T^{* *} with \pi₁(X) finite,

X ( in T_LN) such that \pi₁(X) is torsion-free with all proper subgroups of \pi₁(X) nilpotent,

X ( in T_LN) such that \pi₁(X) is infinite with the maximal condition on normal subgroups of \pi₁(X),

X with \pi₁(X) the Engel group such that whether \pi₁(X) is finite or \pi₁(X) has the maximal conditions for the case \pi₁(X) infinite

then \chi(X) = \chi(Y).

Date received: April 22, 1999