We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from Z2 to Z. We demonstrate how the Z-lift provides a more refined invariant of Legendrian isotopy....

We construct a new invariant of transverse links in the standard contact structure on R3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link, see [4], [13]. Here the knot contact homology of a link in R3 is the Legendrian contact homology DGA of its conormal lift into the unit cotangent bundle S∗R3 of R3, and the filtrations ar...

We consider generic curves in R, i.e. generic C functions f : S → R. We analyze these curves through the persistent homology groups of a filtration induced on S by f . In particular, we consider the question whether these persistent homology groups uniquely characterize f , at least up to re-parameterizations of S. We give a partially positive answer to this question. More precisely, we prove t...

Abstract Serial homology, i.e., homology between repetitive structures in the same individual organism, is a debated concept evolutionary developmental biology. The central question interpretation of “sameness” context body. This essay provides synthetic analysis main issues involved debate, connecting conceptual problems with current experimental research. It argued that serial not all-or-noth...