# Degree of T-equivariant maps in ℝⁿ

Joanna Janczewska; Marcin Styborski

Banach Center Publications (2007)

- Volume: 77, Issue: 1, page 147-159
- ISSN: 0137-6934

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topJoanna Janczewska, and Marcin Styborski. "Degree of T-equivariant maps in ℝⁿ." Banach Center Publications 77.1 (2007): 147-159. <http://eudml.org/doc/281595>.

@article{JoannaJanczewska2007,

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

author = {Joanna Janczewska, Marcin Styborski},

journal = {Banach Center Publications},

keywords = {degree; involution; -equivariant map; gradient map; -homotopic},

language = {eng},

number = {1},

pages = {147-159},

title = {Degree of T-equivariant maps in ℝⁿ},

url = {http://eudml.org/doc/281595},

volume = {77},

year = {2007},

}

TY - JOUR

AU - Joanna Janczewska

AU - Marcin Styborski

TI - Degree of T-equivariant maps in ℝⁿ

JO - Banach Center Publications

PY - 2007

VL - 77

IS - 1

SP - 147

EP - 159

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

LA - eng

KW - degree; involution; -equivariant map; gradient map; -homotopic

UR - http://eudml.org/doc/281595

ER -

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