scholarly journals Equivariant surgery theory: construction of equivariant normal maps

1995 ◽  
Vol 31 (1) ◽  
pp. 145-167 ◽  
Author(s):  
Masaharu Morimoto
Keyword(s):  
Theory Construction ◽  
Surgery Theory ◽  
Equivariant Surgery ◽  
Normal Maps

Equivariant Intersection Theory and Surgery Theory for Manifolds with Middle Dimensional Singular Sets

2008 ◽  
Vol 2 (3) ◽  
pp. 507-600 ◽  
Author(s):  
Anthony Bak ◽  
Masaharu Morimoto
Keyword(s):  
Intersection Theory ◽  
Finite Family ◽  
Dimensional Sphere ◽  
Singular Set ◽  
Intersection Form ◽  
Surgery Theory ◽  
Equivariant Surgery ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Simply Connected

AbstractLet G denote a finite group and n = 2k 6 an even integer. Let X denote a simply connected, compact, oriented, smooth G-manifold of dimension n. Let L denote a union of connected, compact, neat submanifolds in X of dimension k. We invoke the hypothesis that L is a G-subcomplex of a G-equivariant smooth triangulation of X and contains the singular set of the action of G on X. If the dimension of the G-singular set is also k then the ordinary equivariant self-intersection form is not well defined, although the equivariant intersection form is well defined. The first goal of the paper is to eliminate the deficiency above by constructing a new, well defined, equivariant, self-intersection form, called the generalized (or doubly parametrized) equivariant self-intersection form. Its value at a given element agrees with that of the ordinary equivariant self-intersection form when the latter value is well defined. Let denote a finite family of immersions withtrivial normal bundle of k-dimensional, connected, closed, orientable, smooth manifolds into X. Assume that the integral (and mod 2) intersection forms applied to members of and to orientable (and nonorientable) k-dimensional members of L are trivial. Then the vanishing of the equivariant intersection form on × and the generalized equivariant self-intersection form on is a necessary and sufficient condition that is regularly homotopic to a family of disjoint embeddings, each of which is disjoint from L. This property, when is a finite family of immersions of the k-dimensional sphere Sk into X, is just what is needed for constructing an equivariant surgery theory for G-manifolds X as above whose G-singular set has dimension less than or equal to k. What is new for surgery theory is that the equivariant surgery obstruction is defined for an almost arbitrary singular set of dimension k and in particular, the k-dimensional components of the singular set can be nonorientable.

Language and creativity: a Construction Grammar approach to linguistic creativity

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Thomas Hoffmann
Keyword(s):  
Construction Grammar ◽  
Linguistic Theory ◽  
Human Cognition ◽  
Evolutionary Adaptation ◽  
Theory Construction ◽  
Conceptual Blending ◽  
Cognitive Linguistic ◽  
Explanatory Account ◽  
The Way

AbstractCreativity is an important evolutionary adaptation that allows humans to think original thoughts, to find solutions to problems that have never been encountered before and to fundamentally change the way we live. One particular domain of human cognition that has received considerable attention is linguistic creativity. The present paper discusses how the leading cognitive linguistic theory, Construction Grammar, can provide an explanatory account of creativity that goes beyond the issue of linguistic productivity. At the same time, it also outlines how Construction Grammar can benefit from insights from Conceptual Blending.

scholarly journals Contact structures and reducible surgeries

2015 ◽  
Vol 152 (1) ◽  
pp. 152-186 ◽  
Author(s):  
Tye Lidman ◽  
Steven Sivek
Keyword(s):  
Contact Structures ◽  
Surgery Theory ◽  
Contact Topology ◽  
Exceptional Surgery ◽  
Genus 2 ◽  
Cabling Conjecture

We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus$g$must have slope$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.

Sign in / Sign up

Export Citation Format

Share Document