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On the Space of Homeomorphisms of a Compact n ‐manifold
Author(s) -
WONG RAYMOND Y.
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36816.x
Subject(s) - retract , homeomorphism (graph theory) , mathematics , hilbert space , manifold (fluid mechanics) , boundary (topology) , pure mathematics , combinatorics , topology (electrical circuits) , mathematical analysis , mechanical engineering , engineering
In the study of the space of homeomorphisms H ( M ) (with identity on the boundary) of a compact n ‐manifold M (modulo its boundary), the major unsolved problem is whether H ( M ) an absolute neighborhood retract. If the answer is affirmative, then it must be homeomorphic to a Hilbert manifold when combined with known results in infinite‐dimensional topology. It turns out that there is a simple reduction of the problem to the case M being an n ‐ball B. That is, if H ( B ) is an absolute retract, then H ( M ) is an absolute neighborhood retract. We intend to concentrate on the study of H ( B ) and prove that there is dense subset of the space of homeomorphism of the Hilbert cube Q such that each of its member is a finite composition of homeomorphisms that are either Lie in H ( B ) or act in the direction complementary to B.