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- Semi-s-cobordism abstract "In mathematics, a cobordism (W, M, M−) of an (n + 1)-dimensionsal manifold (with boundary) W between its boundary components, two n-manifolds M and M− (n.b.: the original creator of this topic, Jean-Claude Hausmann, used the notation M− for the right-hand boundary of the cobordism), is called a semi-s-cobordism if (and only if) the inclusion is a simple homotopy equivalence (as in an s-cobordism) but the inclusion is not a homotopy equivalence at all.A consequence of (W, M, M−) being a semi-s-cobordism is that the kernel of the derived homomorphism on fundamental groups is perfect. A corollary of this is that solves the group extension problem . The solutions to the group extension problem for proscribed quotient group and kernel group K are classified up to congruence (see Homology by MacLane, e.g.), so there are restrictions on which n-manifolds can be the right-hand boundary of a semi-s-cobordism with proscribed left-hand boundary M and superperfect kernel group K.Note that if (W, M, M−) is a semi-s-cobordism, then (W, M−, M) is a Plus cobordism. (This justifies the use of M− for the right-hand boundary of a semi-s-cobordism, a play on the traditional use of M+ for the right-hand boundary of a Plus cobordism.) Thus, a semi-s-cobordism may be thought of as an inverse to Quillen's Plus construction in the manifold category. Note that (M−)+ must be diffeomorphic (respectively, piecewise-linearly (PL) homeomorphic) to M but there may be a variety of choices for (M+)− for a given closed smooth (respectively, PL) manifold M.".
- Semi-s-cobordism wikiPageExternalLink item=PSPUM-32.
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- Semi-s-cobordism hasPhotoCollection Semi-s-cobordism.
- Semi-s-cobordism subject Category:Algebraic_topology.
- Semi-s-cobordism subject Category:Geometric_topology.
- Semi-s-cobordism subject Category:Homotopy_theory.
- Semi-s-cobordism subject Category:Manifolds.
- Semi-s-cobordism type Artifact100021939.
- Semi-s-cobordism type Conduit103089014.
- Semi-s-cobordism type Manifold103717750.
- Semi-s-cobordism type Manifolds.
- Semi-s-cobordism type Object100002684.
- Semi-s-cobordism type Passage103895293.
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- Semi-s-cobordism type Pipe103944672.
- Semi-s-cobordism type Tube104493505.
- Semi-s-cobordism type Way104564698.
- Semi-s-cobordism type Whole100003553.
- Semi-s-cobordism type YagoGeoEntity.
- Semi-s-cobordism type YagoPermanentlyLocatedEntity.
- Semi-s-cobordism comment "In mathematics, a cobordism (W, M, M−) of an (n + 1)-dimensionsal manifold (with boundary) W between its boundary components, two n-manifolds M and M− (n.b.: the original creator of this topic, Jean-Claude Hausmann, used the notation M− for the right-hand boundary of the cobordism), is called a semi-s-cobordism if (and only if) the inclusion is a simple homotopy equivalence (as in an s-cobordism) but the inclusion is not a homotopy equivalence at all.A consequence of (W, M, M−) being a semi-s-cobordism is that the kernel of the derived homomorphism on fundamental groups is perfect. ".
- Semi-s-cobordism label "Semi-s-cobordism".
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- Semi-s-cobordism sameAs Q7449321.
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- Semi-s-cobordism sameAs Semi-s-cobordism.
- Semi-s-cobordism wasDerivedFrom Semi-s-cobordism?oldid=525867228.
- Semi-s-cobordism isPrimaryTopicOf Semi-s-cobordism.