We describe the space of arrow diagram formulas (defined in [13]) for virtual knot diagrams in the annulus R × S 1 as the kernel of a linear map, inspired from a conjecture due to M. Polyak. As a main application, we slightly improve Grishanov-Vassiliev's theorem for planar chain invariants ([6]).2 Algebraic structures in Gauss diagram invariants theory
We present a new method to produce simple formulas for 1-cocycles of knots over the integers, inspired by Polyak-Viro's formulas for finite-type knot invariants. We conjecture that these 1-cocycles represent finite-type cohomology classes in the sense of Vassiliev. An example of degree 3 is studied, and shown to coincide over Z 2 with the Teiblum-Turchin cocycle v 1 3 .The study of the topology of the space of knots was initiated in 1990 by Vassiliev [23], who defined finite-type cohomology classes by applying ideas from the finitedimensional affine theory of plane arrangements to the infinite-dimensional theory of long knots in 3-space. Here, of finite type means of finite complexity, in some sense, hence hopefully computable. Independently, outstanding general results on the topology of knot spaces have been obtained by Hatcher [11], leading to the idea that higher dimensional invariants of knots -in particular, 1-cocycles -should capture information about the geometry of a knot (see [7]). The zeroth level of Vassiliev's theory, known as finite-type knot invariants, has been extensively studied in the subsequent years [1,2,9,13]. However at the first level -that of 1-cocycles -only one example, in degree 3, has been proved to exist by Teiblum and Turchin, and then actually described by Vassiliev with a formula over Z 2 [22,25]. Since then, no progress has been made, probably because of the technicity of Vassiliev's construction and the apparent difficulty of turning it into a systematic method: indeed, it involves singularity theory with differential geometric 1540004-1 J. Knot Theory Ramifications 2015.24. Downloaded from www.worldscientific.com by CALIFORNIA INSTITUTE OF TECHNOLOGY on 06/27/16. For personal use only.
This research aimed to test the moderating effect of people's initial position to blood donation on the actual acceptance to donate blood in a door-in-the-face situation. This position (attitude, self-importance, normative beliefs) was measured one month prior to the request (Study 1, N = 99) or immediately before (Study 2, N = 80). The results revealed that the doorin-the-face effect is moderated by the importance of blood donation to the self, all the more so when the position is made salient. This highlights the specific character of blood donation in France and the centrality of the importance of donating for the self at the heart of the DITF technique. These results offer new insights into the conditions that must be met to achieve acceptance to donate blood after an initial refusal.
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