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We describe the equivariant cobordism classification of smooth actions of the group on closed smooth m-dimensional manifolds for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with Vⁿ an arbitrary product of spheres and with Vⁿ any n-dimensional closed manifold with n odd.
Pedro L. Q. Pergher. "$Z₂^k$-actions fixing point ∪ Vⁿ." Fundamenta Mathematicae 172.1 (2002): 83-97. <http://eudml.org/doc/282704>.
@article{PedroL2002, abstract = {We describe the equivariant cobordism classification of smooth actions $(M^\{m\},Φ)$ of the group $G = Z₂^k$ on closed smooth m-dimensional manifolds $M^\{m\}$ for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with Vⁿ an arbitrary product of spheres and with Vⁿ any n-dimensional closed manifold with n odd.}, author = {Pedro L. Q. Pergher}, journal = {Fundamenta Mathematicae}, keywords = {-action; equivariant cobordism class; fixed point data; characteristic number; representation}, language = {eng}, number = {1}, pages = {83-97}, title = {$Z₂^k$-actions fixing point ∪ Vⁿ}, url = {http://eudml.org/doc/282704}, volume = {172}, year = {2002}, }
TY - JOUR AU - Pedro L. Q. Pergher TI - $Z₂^k$-actions fixing point ∪ Vⁿ JO - Fundamenta Mathematicae PY - 2002 VL - 172 IS - 1 SP - 83 EP - 97 AB - We describe the equivariant cobordism classification of smooth actions $(M^{m},Φ)$ of the group $G = Z₂^k$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is the union F = p ∪ Vⁿ, where p is a point and Vⁿ is a connected manifold of dimension n with n > 0. The description is given in terms of the set of equivariant cobordism classes of involutions fixing p ∪ Vⁿ. This generalizes a lot of previously obtained particular cases of the above question; additionally, the result yields some new applications, namely with Vⁿ an arbitrary product of spheres and with Vⁿ any n-dimensional closed manifold with n odd. LA - eng KW - -action; equivariant cobordism class; fixed point data; characteristic number; representation UR - http://eudml.org/doc/282704 ER -