Book Review: Applications of algebraic topology
نویسندگان
چکیده
منابع مشابه
Categorically-algebraic topology and its applications
This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...
متن کاملcategorically-algebraic topology and its applications
this paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. it incorporates the most important settings of lattice-valued topology, including poslat topology of s.~e.~rodabaugh, $(l,m)$-fuzzy topology of t.~kubiak and a.~v{s}ostak, and $m$-fuzzy topology on $l$-fuzzy sets of c.~guido. moreover, its respe...
متن کاملApplications of Algebraic Topology to Concurrent Computation
All parallel programs require some amount of synchronization to coordinate their concurrency to achieve correct solutions. It is commonly known that synchronization can cause poor performance by burdening the program with excessive overhead. This chapter develops a connection between certain synchronization primitives and topology. This connection permits the theoretical study of concurrent com...
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Since the invention of quantum logic by Birkhoff & von Neumann there has been a steady interest in the topic. Quantum logic owes much of its current attention to the rise of experimental foundational physics. Many researchers interested in the foundation of physics begin to view this field as a way to understand the quantum better; or at least from a new, hitherto unknown viewpoint. Yet much is...
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We provide a common framework for compatible discretizations using algebraic topology to guide our analysis. The main concept is the natural inner product on cochains, which induces a combinatorial Hodge theory. The framework comprises of mutually consistent operations of differentiation and integration, has a discrete Stokes theorem, and preserves the invariants of the DeRham cohomology groups...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1976
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1976-14102-x