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Degree of $T$-equivariant maps in $\mathbb R^n$

Tom 77 / 2007

Joanna Janczewska, Marcin Styborski Banach Center Publications 77 (2007), 147-159 MSC: 47H11. DOI: 10.4064/bc77-0-11

Streszczenie

A special case of $G$-equivariant degree is defined, where $G=\mathbb Z_2$, and the action is determined by an involution $T:\mathbb R^p\oplus\mathbb R^q\to\mathbb R^p\oplus\mathbb R^q$ given by $T(u,v)=(u,-v)$. The presented construction is self-contained. It is also shown that two $T$-equivariant gradient maps $f,g:(\mathbb R^n,S^{n-1})\to(\mathbb R^n,\mathbb R^n\setminus\{0\})$ are $T$-homotopic iff they are gradient $T$-homotopic. This is an equivariant generalization of the result due to Parusi/nski.

Autorzy

  • Joanna JanczewskaDepartment of Technical Physics and Applied Mathematics
    Gdańsk University of Technology
    Narutowicza 11/12
    80-952 Gdańsk , Poland
    e-mail
  • Marcin StyborskiDepartment of Technical Physics and Applied Mathematics
    Gdańsk University of Technology
    Narutowicza 11/12
    80-952 Gdańsk , Poland
    and
    Ph.D. student of the Institute of Mathematics
    Polish Academy of Sciences
    e-mail

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