Year: 2026
Type: preprint
Abstract: We define the notion of weighted polyhedron which can be thought of as the geometric realization of a weighted simplicial complex introduced by Dawson. Moreover, we will define a weighted version of singular homology theory for a weighted polyhedron and prove that it is isomorphic to the weighted simplicial homology of the weighted polyhedron. This implies that weighted simplicial homology is an invariant under isomorphisms and more generally under certain type of homotopy equivalences of weighted polyhedra. Moreover, we will generalize the cup product and cap product to weighted singular cohomology. In addition, we will interpret some known theories of orbifolds in terms of our weighted singular homology and cohomology.
Source: arXiv (Cornell University)
Institution: Shandong University of Science and Technology
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G243180679
OpenAlex ID: W7204883678