1,721,019 research outputs found
-stable classification of -manifolds with finite fundamental group
Full text linkWe show that two closed, connected -manifolds with finite fundamentalgroups are -stably homeomorphic if and only if their quadratic-types are stably isomorphic and their Kirby-Siebenmann invariant agrees.<br
Embedding surfaces in 4-manifolds
Full text linkWe prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a combinatorial formula for its computation. For this we introduce the notion of band characteristic surfaces.56 pages, 20 figures; in v2, we have added a new section (Section 1.5) containing applications to knot theory; v3: several minor changes and corrections following a referee report, to appear in Geometry & Topolog
Four-manifolds up to connected sum with complex projective planes
Full text linkWe show that closed, connected 4-manifolds up to connected sum with copies of
the complex projective plane are classified in terms of the fundamental group,
the orientation character and an extension class involving the second homotopy
group. For fundamental groups that are torsion free or have one end, we reduce
this further to a classification in terms of the homotopy 2-type.Comment: 37 pages. v2: former sections 5 and 6 rewritten and split into
current sections 5, 6, and 7. Accepted for publication in American Journal of
Mathematic
The Kervaire-Milnor invariant in the stable classification of spin 4-manifolds
Full text linkWe consider the role of the Kervaire–Milnor invariant in the classification of closed, connected, spin 4-manifolds, typically denoted by M, up to stabilisation by connected sums with copies of S2 x S2. This stable classification is detected by a spin bordism group over the classifying space Bπ of the fundamental group. Part of the computation of this bordism group via an Atiyah–Hirzebruch spectral sequence is determined by a collection of codimension-two Arf invariants. We show that these Arf invariants can be computed by the Kervaire–Milnor invariant evaluated on certain elements of π2 (M). In particular this yields a new stable classification of spin 4-manifolds with 2-dimensional fundamental groups, namely those for which Bπ admits a finite 2-dimensional CW-complex model
Algebraic Criteria for Stable Diffeomorphism of Spin 4-manifolds
No full textWe study closed, connected, spin 4-manifolds up to stabilisation by connected sums with copies of S2 x S2. For a fixed fundamental group, there are primary, secondary and tertiary obstructions, which together with the signature lead to a complete stable classification. The primary obstruction exactly detects CP2-stable diffeomorphism and was previously related to algebraic invariants by Kreck and the authors. In this article we formulate conjectural relationships of the secondary and tertiary obstructions with algebraic invariants: the secondary obstruction should be determined by the (stable) equivariant intersection form and the tertiary obstruction via a -invariant recording intersection data between 2-spheres, with trivial algebraic self-intersection, and their Whitney discs. We prove our conjectures for the following classes of fundamental groups: groups of cohomological dimension at most 3, right-angled Artin groups, abelian groups, and finite groups with quaternion or abelian 2-Sylow subgroups. We apply our theory to give a complete algebraic stable classification of spin 4-manifolds with fundamental group Z x Z/2
Stable classification of 4-manifolds with 3-manifold fundamental groups
Full text linkWe study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w2-type and their equivariant intersection forms are stably isometric. We also find explicit algebraic invariants that determine the stable classification for spin manifolds in this class
Immersions of punctured 4-manifolds: with applications to quantum cellular automata
No full textMotivated by applications to pulling back quantum cellular automata from one manifold to another, we study the existence of immersions between certain smooth 4-manifolds. We show that they lead to a very interesting partial order on closed 4-manifold
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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