Browder-Livesay Groups of Abelian 2-Groups

Muranov, Yu. V.; Kharshiladze, A. F.

doi:10.1070/sm1991v070n02abeh001261

Cited by 17 publications

(23 citation statements)

References 11 publications

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“…In case of abelian groups Φ = ±1 and d\ = 1 ± 1, and so the torsion part goes to the ^2-terrn unchanged. In fact in cases 1) and 3) when the LJV-groups do not contain a free part, E\ = £Όο (see the diagrams at the end of [12]). Consider the only remaining case, 2).…”

Section: Ln 2n (N ^G) = (Z/2 F-'-r -(I)mentioning

confidence: 99%

“…The Browder-Livesay groups LN n (n -> G) for this case (with prime decoration) are given in [12], as well as a lot of information about the natural maps between Wall and Browder-Livesay groups. Denote as usual by r the 2-rank of G, and by s the number of Z/2 direct summands in G. There are three cases:…”

Section: Which Is Equal To 1 + (-L) P+l W(t)mentioning

confidence: 99%

“…All natural maps between different Wall and Browder-Livesay groups can be located in the following braid (i: π -* G is the inclusion): (1) This braid was considered from the topological and algebraic viewpoints in [11], [4], [6], [9], [10], [12]; it is the main tool for the construction of iterated BrowderLivesay invariants.…”

Section: (V Dv) Of Manifolds With Boundaries and DV = υ Then D(y) mentioning

confidence: 99%

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A Spectral Sequence in Surgery

Khèmblton¹,

Kharshiladze²

1994

Russ. Acad. Sci. Sb. Math.

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Section: Ln 2n (N ^G) = (Z/2 F-'-r -(I)mentioning

confidence: 99%

Section: Which Is Equal To 1 + (-L) P+l W(t)mentioning

confidence: 99%

Section: (V Dv) Of Manifolds With Boundaries and DV = υ Then D(y) mentioning

confidence: 99%

See 1 more Smart Citation

A Spectral Sequence in Surgery

Khèmblton¹,

Kharshiladze²

1994

Russ. Acad. Sci. Sb. Math.

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“…The algebraic construction of diagram (10) for quadratic extensions of anti-structures was given in [33]. In this case, diagram (10) can be efficiently used for calculation of obstruction groups and natural mappings in L-theory (see [7,8,14,34]). Moreover, diagram (10) allows one to obtain deep geometric results on representability of elements of Wall groups by normal mappings of closed manifolds (see [16,17,30,35]).…”

Section: Splitting Obstruction Groups and L-spectramentioning

confidence: 99%

Splitting along Submanifolds and L-Spectra

Bak¹,

Muranov²

2004

Journal of Mathematical Sciences

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Abstract. The problem of splitting of homotopy equivalence along a submanifold is closely related to surgeries of submanifolds and exact sequences in surgery theory. We describe possibilities and methods of application of L-spectra for the investigation of the problem of splitting of (simple) homotopy equivalence of manifolds along submanifolds. This approach naturally leads us to commutative diagrams of exact sequences, which play an important role in calculational problems of surgery theory.

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“…This diagram has been studied from algebraic and geometric viewpoints in many papers (see [2,3,4,5,6,9,12,21,23,31]). …”

Section: Introductionmentioning

confidence: 99%

A spectral sequence in surgery theory and manifolds with filtrations

Muranov

Repovš

Jiménez

2006

Trans. Moscow Math. Soc.

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Abstract. In 1978 Cappell and Shaneson pointed out interesting properties of the Browder-Livesay invariants, which are analogous to the differentials of a certain spectral sequence. Such a spectral sequence was constructed by Hambleton and Kharshiladze in 1991. The main step of the construction of the spectral sequence consists in constructing an infinite filtration of spectra, in which, as is well known, only the first two spectra have a clear geometric meaning. In the present paper a geometric interpretation is given to all the spectra of the filtration in the Hambleton-Kharshiladze construction. Surgery obstruction groups for a system of embedded manifolds are introduced, and it is proved that the spectra realizing these groups coincide with the spectra in the Hambleton-Kharshiladze filtration. The algebraic and geometric properties of these groups and their connections with classical surgery theory are described. An isomorphism between these groups and the Browder-Quinn surgery obstruction groups for stratified manifolds is established. The results obtained are applied to the problem of realization of elements of the Wall groups by normal maps of closed manifolds and to the study of the iterated Browder-Livesay invariants.

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Browder-Livesay Groups of Abelian 2-Groups

Cited by 17 publications

References 11 publications

A Spectral Sequence in Surgery

A Spectral Sequence in Surgery

Splitting along Submanifolds and L-Spectra

A spectral sequence in surgery theory and manifolds with filtrations

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