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Bords homotopiques et modèles de Quillen - Kahl, Thomas; Lambrechts, Pascal; Vandembroucq, Lucile
A homotopy boundary of a finite simply connected CW complex $X$ is the boundary of a compact manifold of the homotopy type of $X$. We study the rational homotopy type of the homotopy boundaries of $X$ using Quillen models and we show, in particular, that a large class of homotopy boundaries of $X$ is rationally determined by the rational homotopy type of $X$.
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Homotopy invariance in E-theory - Thomsen, Klaus
We introduce equivalence relations among asymptotic homomorphisms that in general are stronger than homotopy, but which we show are equivalent to homotopy when the domain is a suspended $C\sp *$-algebra. As an application, we show that the E-theory of Connes and Higson can be realized as a special case of Kasparovs KK-theory.
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Matrices and finite biquandles - Nelson, Sam; Vo, John
We describe away of representing finite biquandles with $n$ elements as $2n \times 2n$ block matrices. Any finite biquandle defines an invariant of virtual knots through counting homomorphisms. The counting invariants of non-quandle biquandles can reveal information not present in the knot quandle, such as the nontriviality of the virtual trefoil and various Kishino knots. We also exhibit an oriented virtual knot which is distinguished from both its obverse and its reverse by a finite biquandle counting invariant. We classify biquandles of order 2, 3 and 4 and provide a URL for our Maple programs for computing with finite biquandles.
5.
Homology with local coefficients and characteristic classes - Greenblatt, Robert
In this thesis, we are concerned with the study of cohomology with local coefficients and applications to (non-orientable) real vector bundles. The thesis consists of an introduction and three separate sections. The introduction gives some motivation for considering cohomology with local coefficients and an outline of the results obtained. The first section deals with a general discussion of such cohomology groups and contains a Künneth Theorem for such groups. The second section is devoted to some computations which are needed later and the final section gives a complete description of the integral cohomology of the spaces $BO(n)$ and $BSO(n)$.
7.
Deformations of associative algebras with inner products - Terilla, John; Tradler, Thomas
We develop the deformation theory of $A\sb \infty$ algebras together with $\infty$-inner products and identify a differential graded Lie algebra that controls the theory. This generalizes the deformation theories of associative algebras, $A\sb \infty$ algebras, associative algebras with inner products, and $A\sb \infty$ algebras with inner products.
11.
Support varieties: an ideal approach - Buan, Aslak Bakke; Krause, Henning; Solberg, Øyvind
We introduce equivalence relations among asymptotic homomorphisms that in general are stronger than homotopy, but which we show are equivalent to homotopy when the domain is a suspended $C\sp *$-algebra. As an application, we show that the E-theory of Connes and Higson can be realized as a special case of Kasparovs KK-theory.
12.
$rec.titulo - Noohi, Behrang
This paper contains some basic results on 2-groupoids, with special emphasis on computing derived mapping 2-groupoids between 2-groupoids and proving their invariance under strictification. Some of the results proven here are presumably folklore (but do not appear in the literature to the authors knowledge) and some of the results seem to be new. The main technical tool used throughout the paper is the Quillen model structure on the category of 2-groupoids introduced by Moerdijk and Svensson.
14.
3-types of simplicial groups and braided regular crossed modules - Arvasi, Z.; Ulualan, E.
In this work, we explain the relations among braided regular crossed modules, simplicial groups, 2-crossed modules, quadratic modules and crossed squares, and the role of hypercrossed complex pairings in these structures.
17.
Hyperarbres, arbres eracinés et partitions pointés - Chapoton, F.
We compute the characteristic polynomials of the posets of hypertrees. We show that the generating series of the polynomials can be expressed using cyclic hypertrees. We also propose a conjecture on the action of symmetric groups on the Whitney homology of these posets. In addition, we show that Vallettes poset of pointed partitions is homotopy equivalent to Pitmans poset of forests. The implicit common theme of these topics is the combinatorics of the PreLie operad.
19.
The fundamental weighted category of a weighted space: From directed to weighted algebraic topology - Grandis, Marco
We want to investigate spaces where paths have a weight, or cost, expressing length, duration, price, energy, etc. The weight function is not assumed to be invariant up to pathreversion. Thus, weighted algebraic topology can be developed as an enriched version of directed algebraic topology, where illegal paths are penalised with an infinite cost, and the legal ones are measured. Its algebraic counterpart will be weighted algebraic structures, equipped with a sort of directed seminorm.
¶ In the fundamental weighted category of a generalised metric space, introduced here, each homotopy class of paths has a weight (or seminorm), which is subadditive...
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