Canonical isotopies in Euclidean space |
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Authors: | Bjorn Friberg |
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Institution: | (1) Department of Mathematics, University of saskatchewan, Saskatoon, Saskatchewan, Canada |
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Abstract: | LetG(n,k) denote the space (with the compact-open topology) of homeomorphisms ofR
n which are fixed onR
k. Theorem 1:G(n, n−2) deforms inG(n, 0) toO(2), whereO(2) is the orthogonal group. Corollary 2: (forn=2) the Kneser theorems. Corollary 3: A EuclideanR
n bundleξ
n
overS
m(m≦∞) which contains anR
n−2 subbundleξ
n − 2 is isomorphic, as aG(n,0) bundle, to a Whitney sumξ
n − 2 ⊕ξ
2. Corollary 4: (n−2) stable homeomorphisms ofR
n orS
n are (n−1) stable, hence stable if orientation preserving.
Part of this work represents a portion of the author’s Ph.D. thesis at the University of California, Los Angeles, written
under the direction of D. S. Gillman and R. C. Kirby. |
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Keywords: | |
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