Infinite Regular Neighbourhoods

Scott, Anne Firor

doi:10.1112/jlms/s1-42.1.245

“…An equivariant PL map /: My -» M2 is called equivariantly tangential if tA7, © 9k ^G/*(rM2) © 0\ where tM,, tM2 are tangent G PL microbundles over Mx, M2, respectively (we refer to [7] for more information about G-microbundles). By simple modifications one can generalize Theorems 1 and 2 of [15] to the case of G PL manifolds. In particular, we have the following (see [14]) Theorem 5.2.…”

Section: Definitionmentioning

confidence: 99%

Tangential Equivalence of Group Actions

Kwasik¹

1984

Transactions of the American Mathematical Society

0

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We consider the problem of tangential equivalence of group actions on manifolds. In particular we discuss a conjecture of B. Mazur and its modifications. The negative answer to this conjecture is presented. On the other hand we prove that the "isovariant" version of this conjecture, as well as the modified one, remains true.As an application some results on the tangential equivalence of Zp-actions on homotopy spheres are obtained.

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“…An equivariant PL map /: My -» M2 is called equivariantly tangential if tA7, © 9k ^G/*(rM2) © 0\ where tM,, tM2 are tangent G PL microbundles over Mx, M2, respectively (we refer to [7] for more information about G-microbundles). By simple modifications one can generalize Theorems 1 and 2 of [15] to the case of G PL manifolds. In particular, we have the following (see [14]) Theorem 5.2.…”

Section: Definitionmentioning

confidence: 99%

Tangential equivalence of group actions

Kwasik¹

1984

Trans. Amer. Math. Soc.

1

0

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Abstract. We consider the problem of tangential equivalence of group actions on manifolds. In particular we discuss a conjecture of B. Mazur and its modifications. The negative answer to this conjecture is presented. On the other hand we prove that the "isovariant" version of this conjecture, as well as the modified one, remains true.As an application some results on the tangential equivalence of Zp-actions on homotopy spheres are obtained.

show abstract

“…Spivak's argument is complicated by allowing the degree of the covering to be infinite. In such cases the space K is non-compact and the inclusion K → R k+c requires a further stabilisation, by increasing the codimension, in order to imbed K as proper polyhedral subset and so construct a genuine infinite regular neighbourhood in the sense, for example, of [25]. This elaboration is unnecessary when the degree of the covering map is finite.…”

mentioning

confidence: 99%