In mathematics, the plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups.
Explicitly, if is a based connected CW complex and is a perfect normal subgroup of then a map is called a +-construction relative to if induces an isomorphism on homology, and is the kernel of .[1]
The plus construction was introduced by Michel Kervaire (1969), and was used by Daniel Quillen to define algebraic K-theory. Given a perfect normal subgroup of the fundamental group of a connected CW complex , attach two-cells along loops in whose images in the fundamental group generate the subgroup. This operation generally changes the homology of the space, but these changes can be reversed by the addition of three-cells.
The most common application of the plus construction is in algebraic K-theory. If is a unital ring, we denote by the group of invertible -by- matrices with elements in . embeds in by attaching a along the diagonal and s elsewhere. The direct limit of these groups via these maps is denoted and its classifying space is denoted . The plus construction may then be applied to the perfect normal subgroup of , generated by matrices which only differ from the identity matrix in one off-diagonal entry. For , the -th homotopy group of the resulting space, , is isomorphic to the -th -group of , that is,
^Charles Weibel, An introduction to algebraic K-theory IV, Definition 1.4.1
In mathematics, the plusconstruction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups...
and decarbonise the construction sector, including recommendations for engineers, the construction industry and decision makers, plus outlined six-overarching...
plus contract states that a client agrees to reimburse a construction company for building expenses such as labor, materials, and other costs, plus additional...
The PLUS Expressways Berhad (MYX: 5052) is the largest highway concessionaries or build–operate–transfer operator company in Malaysia. A member of the...
Company plus four Construction Companies: A, B, C, & D. CBs are organized to function as independent self sufficient units. Regiment: Naval Construction Regiments...
ambiguity with the ne … plusconstruction when written down, as plus could mean either more or not anymore. Generally when plus is used to mean more, the...
for paying that amount whether the construction project exceeds or falls below the agreed price of payment. Cost plus fee: This contract provides payment...
consisting of a straightening and widening of Atamyrat Nyýazow şaýoly plusconstruction of 13 high-rise apartment buildings, two secondary schools, two kindergartens...
Vaughan Jones construction Strähle construction Coset constructionPlusconstruction Algebraic K-theory Gelfand–Naimark–Segal construction Stanley–Reisner...
Materials Management in Construction Projects". www.nbmcw.com. Retrieved 2021-09-21. "4 Types of Construction Projects (PlusConstruction Careers)". Indeed...
equipment, hazardous substances, plus the effects of excessive noise, dust and vibration. The leading causes of construction site fatalities are falls, electrocutions...
The construction of the first World Trade Center complex in New York City was conceived as an urban renewal project to help revitalize Lower Manhattan...
2020. "Construction contracts awarded for new Austria Lustenau stadium". thestadiumbusiness.com. 5 October 2023. "Ces sept clubs de foot sont plus écolos...
The Plus 15 or +15 is a skyway network in Calgary, Alberta, Canada. It is the world's most extensive pedestrian skywalk system, with a total length of...
are: "we had arrived"; "they had written". The word derives from the Latin plus quam perfectum, "more than perfect". The word "perfect" in this sense means...
In fact, Suslin (1981) showed that X yields a model for Quillen's plus-construction B G L ( R ) / X ≃ B G L + ( R ) {\displaystyle BGL(R)/X\simeq BGL^{+}(R)}...
Construction News is a monthly publication, plus digital and events services, primarily targeting the United Kingdom construction industry. The magazine...
catalogs as 6lobe (starting with the numeral 6, not the capital letter G). Torx Plus, Torx Paralobe and Torx ttap are improved head profiles. Torx screws are...
"intention of Parliament", and the English courts developed three main rules (plus some minor ones) to assist them in the task. These were: the mischief rule...
cum infinitivo or accusative plus infinitive, frequently abbreviated ACI or A+I) is the name for a syntactic construction first described in Latin and...
spans. The works included the movement of existing rail sidings; plusconstruction of new general and coaling sidings, east of the dock. The dock was...