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Lecture

Cellular structure of the torus with two holes

In course

MATH-225: Topology II - fundamental groups

On étudie des notions de topologie générale: unions et quotients d'espaces topologiques; on approfondit les notions de revêtements et de groupe fondamental,et d'attachements de cellules et on démontre le Théorème de Seifert-van Kampen. Des exemples de surf ...

Description

This lecture explains the cellular structure of the torus with two holes, obtained by summing two simple tori. Starting from the torus boundary, it constructs a wedge of four circles, then adds a 2-cell to form the torus. The attachment process is described using an octagon and the fundamental group of a wedge of four circles.

Instructors (2)

Dimitri Stelio Wyss

Jérôme Scherer

Official source

Related concepts (19)

Attachment theory

Attachment theory is a psychological, evolutionary and ethological theory concerning relationships between humans. The most important tenet is that young children need to develop a relationship with at least one primary caregiver for normal social and emotional development. The theory was formulated by psychiatrist and psychoanalyst John Bowlby. Within attachment theory, infant behaviour associated with attachment is primarily the seeking of proximity to an attachment figure in stressful situations.

Attachment therapy

Attachment therapy (also called "the Evergreen model", "holding time", "rage-reduction", "compression therapy", "rebirthing", "corrective attachment therapy", and "coercive restraint therapy") is a pseudoscientific child mental health intervention intended to treat attachment disorders. It is found primarily in the United States, and much of it is centered in about a dozen clinics in Evergreen, Colorado, where Foster Cline, one of the founders, established his clinic in the 1970s.

Attachment in children

Attachment in children is "a biological instinct in which proximity to an attachment figure is sought when the child senses or perceives threat or discomfort. Attachment behaviour anticipates a response by the attachment figure which will remove threat or discomfort". Attachment also describes the function of availability, which is the degree to which the authoritative figure is responsive to the child's needs and shares communication with them.

Reactive attachment disorder

Reactive attachment disorder (RAD) is described in clinical literature as a severe and relatively uncommon disorder that can affect children, although these issues do occasionally persist into adulthood. RAD is characterized by markedly disturbed and developmentally inappropriate ways of relating socially in most contexts. It can take the form of a persistent failure to initiate or respond to most social interactions in a developmentally appropriate way—known as the "inhibited form".

Cell potency

Cell potency is a cell's ability to differentiate into other cell types. The more cell types a cell can differentiate into, the greater its potency. Potency is also described as the gene activation potential within a cell, which like a continuum, begins with totipotency to designate a cell with the most differentiation potential, pluripotency, multipotency, oligopotency, and finally unipotency. Totipotency (Lat. totipotentia, "ability for all [things]") is the ability of a single cell to divide and produce all of the differentiated cells in an organism.

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