Homological connectivity is a concept from algebraic topology and homological algebra that relates to how well-connected a topological space or algebraic object is in terms of its homological properties. It can involve examining the relationships between different homology groups of a space. In a more specific context, homological connectivity can refer to the lowest dimension in which the homology groups of a space are nontrivial.

Sobolev mapping refers to the concept of mappings (or functions) between two spaces that belong to Sobolev spaces, which are a class of function spaces that consider both the functions and their weak derivatives.

A Postnikov system is a concept in algebraic topology, specifically in the study of homotopy theory. It is a type of construction used to analyze the homotopy type of a space by breaking it down into simpler pieces that reflect certain homotopical features. More formally, a Postnikov system consists of a tower of spaces and maps that encode the information of the homotopy groups of a space.

AFGL 2591, also known as IRAS 20126+4104, is an astronomical object located in the constellation Cassiopeia. It is a proto-planetary nebula, which is a phase in the evolution of a star similar to our Sun that is transitioning away from the asymptotic giant branch phase. This nebula is notable for exhibiting features typical of these types of objects, including a central star that is surrounded by expanding gas and dust.

The Excision Theorem is a fundamental result in algebraic topology, particularly in the context of singular homology. It addresses how the homology groups of a topological space can be affected by the removal of a "nice" subspace.

The Mayer–Vietoris sequence is a fundamental tool in algebraic topology, particularly in the study of singular homology and cohomology theories. It provides a way to compute the homology or cohomology of a topological space from that of simpler subspaces.

Polar homology is an algebraic concept that arises in the study of commutative algebra and algebraic geometry, particularly in the context of the theory of Gröbner bases and polynomial ideals. Polar homology can be thought of as a homology theory that is related to the structure of a polynomial ring, considering the "polar" aspects of a given polynomial or collection of polynomials.

Reduced homology is a variant of standard homology theory in algebraic topology, typically applied to topological spaces. It is particularly useful for spaces that are not simply connected or that have certain types of singularities, as it helps to simplify some aspects of their homological properties.

Adams filtration is a concept in homotopy theory, particularly in the study of stable homotopy groups of spheres and related areas. It is named after the mathematician Frank Adams, who developed this theory in the mid-20th century. Adams filtration is associated with the idea of understanding the stable homotopy category through a hierarchical structure that helps in studying and organizing the stable homotopy groups of spheres.

The Steenrod problem, named after mathematician Norman Steenrod, refers to a question in the field of algebraic topology concerning the properties and structure of cohomology operations. Specifically, it deals with the problem of determining which cohomology operations can be represented by "natural" cohomology operations on spaces, particularly focusing on the stable homotopy category.

As of my last knowledge update in October 2021, the tallest players in NBA history are: 1. **Gheorghe Mureșan** - 7 feet 7 inches (231 cm) 2. **Yao Ming** - 7 feet 6 inches (229 cm) 3. **Manute Bol** - 7 feet 7 inches (231 cm) 4. **Shawn Bradley** - 7 feet 6 inches (229 cm) 5.

As of my last knowledge update in October 2023, the list of the verified shortest people includes individuals who have been certified by Guinness World Records for their height. Here are a few of the shortest verified individuals: 1. **Chandra Bahadur Dangi (Nepal)** - He was recognized as the shortest adult man in recorded history, measuring 54.6 cm (21.5 in) tall.

The Halperin conjecture is a statement in the field of topology, specifically relating to the study of CW complexes and their homotopy groups. Formulated by the mathematician and topologist Daniel Halperin in the 1970s, the conjecture predicts certain properties regarding the homotopy type of a space based on the behavior of its fundamental group and higher homotopy groups.

The Homotopy Hypothesis, often discussed in the context of higher category theory and homotopy theory, is a conjecture in mathematics concerning the relationship between homotopy types and higher categorical structures. It essentially posits that certain categories, specifically (\(\infty\)-categories), can be equivalently described in terms of homotopy types.

The Hopf invariant is a topological invariant that arises in the study of mappings between spheres, particularly in the context of homotopy theory and homotopy groups of spheres. Named after Heinz Hopf, the invariant provides a way to classify certain types of mappings and can be used to distinguish between different homotopy classes of maps.

A **model category** is a concept from category theory, which is a branch of mathematics that deals with abstract structures and relationships between them. Specifically, a model category provides a framework for doing homotopy theory in a categorical setting. It allows mathematicians to work with "homotopical" concepts such as homotopy equivalences, fibrations, and cofibrations in a systematic way.

Michael A. Wartell is an academic known for his work in the field of computer science, particularly in the area of computer networking and systems. He has held positions in academia, including serving as a dean or provost at various universities.

Anthropometric history is a field of study that examines the physical measurements and characteristics of human populations over time, often focusing on height, weight, body mass index (BMI), and other health-related metrics. This discipline is concerned with understanding how these measurements relate to various socio-economic, environmental, and cultural factors, thus providing insights into the living conditions, health, and nutritional status of populations across different historical periods.

The Sullivan conjecture, proposed by mathematician Dennis Sullivan in the 1970s, pertains to the areas of topology and dynamical systems. Specifically, it deals with the interaction between topology and algebraic geometry concerning the existence of certain types of invariants. The conjecture states that any two homotopy equivalent aspherical spaces have homeomorphic fundamental groups.

In homotopy theory, the concept of *weak equivalence* is central to the study of topological spaces and their properties under continuous deformations. Two spaces (or more generally, two objects in a suitable category) are said to be weakly equivalent if they have the same homotopy type, meaning there exists a continuous mapping between them that induces isomorphisms on all homotopy groups.