Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska; Marcin Styborski

Banach Center Publications, Tome 75 (2007), p. 147-159 / Harvested from The Polish Digital Mathematics Library

Résumé

A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution $T : ℝ^{p} \oplus ℝ^{q} \to ℝ^{p} \oplus ℝ^{q}$ given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps $f, g : (ℝ ⁿ, S^{n - 1}) \to (ℝ ⁿ, ℝ ⁿ ∖ 0)$ are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.

Publié le : 2007-01-01

Zbl 1121.47043

EUDML-ID : urn:eudml:doc:281595

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     author = {Joanna Janczewska and Marcin Styborski},
     title = {Degree of T-equivariant maps in Rn},
     journal = {Banach Center Publications},
     volume = {75},
     year = {2007},
     pages = {147-159},
     zbl = {1121.47043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-11}
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Joanna Janczewska; Marcin Styborski. Degree of T-equivariant maps in ℝⁿ. Banach Center Publications, Tome 75 (2007) pp. 147-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc77-0-11/