Fundamental groups of simplicial complexes
نویسندگان
چکیده
منابع مشابه
Critical Groups of Simplicial Complexes
We generalize the theory of critical groups from graphs to simplicial complexes. Specifically, given a simplicial complex, we define a family of abelian groups in terms of combinatorial Laplacian operators, generalizing the construction of the critical group of a graph. We show how to realize these critical groups explicitly as cokernels of reduced Laplacians, and prove that they are finite, wi...
متن کاملFundamental Properties of Digital Simplicial Homology Groups
In this article we give characteristic properties of the simplicial homology groups of digital images which are based on the simplicial homology groups of topological spaces in algebraic topology. We then investigate EilenbergSteenrod axioms for the simplicial homology groups of digital images. We state universal coefficient theorem for digital images. We conclude that the Künneth formula for s...
متن کاملAlgebraic fundamental group and simplicial complexes
In this paper we prove that the fundamental group of a simplicial complex is isomorphic to the algebraic fundamental group of its incidence algebra, and we derive some applications. AMS classification : 16E40 ; 16G20 ; 06A11 ; 55Q05 Let k be a field and A be a basic and split finite dimensional k-algebra, which means that A/r = k× k× . . .× k where r is the radical of A. There exists a unique q...
متن کاملEfficient Computation in Groups and Simplicial Complexes
Using HNN extensions of the Boone-Britton group, a group E is obtained which simulates Turing machine computation in linear space and cubic time. Space in E is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators required to convert one word to another. The space bound is used to derive a PSPACE-complete problem for a topol...
متن کاملThe Fundamental Group of Balanced Simplicial Complexes and Posets
We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2017
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2017.01.023