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• Regular homotopy group of immersions (Ex)
  ...this exercise is to get more feeling for the regular homotopy group of $k$-immersions in $M$, $I_k(M)$ and the intersection/self-intersection form on it. Below a ...is defined as follows. Elements of $I_k(M)$ are represented by pointed $k$-immersions, i.e pairs $(f,w)$ with $f:S^k\looparrowright M$ is an immersion which does
  3 KB (540 words) - 12:58, 1 April 2012
• Intersection number of immersions
  ...mersions have. The intersection number is an obstruction to perturbing the immersions into being disjoint. When it vanishes this perturbation can often be achiev Immersions $f_1$ and $f_2$ are ''transverse'' (or have ''transverse intersection'') if
  3 KB (467 words) - 13:17, 2 April 2019
• Equivariant intersection number of π-trivial immersions
  ...mersions have. The intersection number is an obstruction to perturbing the immersions into being disjoint, which when zero can often be achieved using the Whitne ... \looparrowright M^{n_1+n_2}$ be transverse [[Π-trivial_map|$\pi$-trivial immersions]] of oriented manifolds with prescribed lifts $\widetilde{f}_1:N_1^{n_1} \l
  7 KB (1,269 words) - 13:34, 16 June 2014

Page text matches

• Embeddings in Euclidean space: an introduction to their classification
  [[Immersions: classification]]
  34 KB (5,424 words) - 07:01, 6 November 2021
• Embeddings just below the stable range: classification
  (Here is sketch of an argument. Using the Smale-Hirsch classification of immersions we obtain that restrictions of $f$ and $f_0$ to $N_0$ are `regular homotopi
  33 KB (5,787 words) - 04:46, 1 September 2021
• Quadratic forms for surgery
  ...is $1$-connected. Let $$I_q(M)$$ be the set of regular homotopy classes of immersions $S^q \to M$ which represent elements of the surgery kernel $K_q(M)$ (with r ... \to \Bbb Z_2 $$ is homotopy invariant. That is, if $a,b: S^q \to M$ are immersions representing the same element $x \in K_q(M)$, then $\mu'(a) = \mu'(b)$).
  4 KB (733 words) - 16:04, 29 April 2016
• Intersection form
  ...ticular case is [[Intersection_number_of_immersions|intersection number of immersions]].
  14 KB (2,390 words) - 10:32, 16 December 2023
• Hirsch-Smale theory
  A regular homotopy of immersions $f_0,f_1:A \rightarrow N$ is a homotopy $h:f_0 \simeq f_1:A \rightarrow N$ ... of regular homotopy classes of immersions and more generally the space of immersions via their derivative maps. It is one of the spectacular success stories of
  3 KB (588 words) - 05:46, 7 December 2012
• Regensburg Surgery Blockseminar 2012: Program
  ... a black box but give more examples of sets of regular homotopy classes of immersions, in particular $\text{Imm}(S^n, S^{2n})$. State and prove Theorems 3.59 an ...nd Theorem 4.8. Draw lots of pictures. Find and present some examples of immersions with interesting self-intersections.
  8 KB (1,194 words) - 15:42, 9 May 2012
• Regensburg Surgery Blockseminar 2012: Exercises
  *[[Regular homotopy group of immersions (Ex)]]
  2 KB (206 words) - 19:07, 25 August 2013
• Regular homotopy group of immersions (Ex)
  ...this exercise is to get more feeling for the regular homotopy group of $k$-immersions in $M$, $I_k(M)$ and the intersection/self-intersection form on it. Below a ...is defined as follows. Elements of $I_k(M)$ are represented by pointed $k$-immersions, i.e pairs $(f,w)$ with $f:S^k\looparrowright M$ is an immersion which does
  3 KB (540 words) - 12:58, 1 April 2012
• Oberwolfach Surgery Seminar 2012: General information
  ...erwolfach Surgery Seminar 2012: Program#L-groups of rings with involution|Immersions, the Wall form and formations]] [[User:Diarmuid Crowley|DC]]: [http://www.d
  8 KB (1,000 words) - 09:47, 6 August 2012
• Immersion
  #''Classification'': How many ''`essentially different´'' immersions exist? ... homotopy equivalence. Here the space, $\textup{Imm}(M, N)$, of all smooth immersions $f : M \looparrowright N $ and $\textup{Mono}(TM, TN)$, the space of all ve
  7 KB (1,187 words) - 12:15, 16 May 2013
• Embedding
  of local flatness is implied by our definition of immersion. Embeddings (and immersions) into familiar target manifolds such as $\R^n$ may help to visualize abstra
  3 KB (517 words) - 07:56, 15 March 2019
• Intersection number of immersions
  ...mersions have. The intersection number is an obstruction to perturbing the immersions into being disjoint. When it vanishes this perturbation can often be achiev Immersions $f_1$ and $f_2$ are ''transverse'' (or have ''transverse intersection'') if
  3 KB (467 words) - 13:17, 2 April 2019
• Equivariant intersection number of π-trivial immersions
  ...mersions have. The intersection number is an obstruction to perturbing the immersions into being disjoint, which when zero can often be achieved using the Whitne ... \looparrowright M^{n_1+n_2}$ be transverse [[Π-trivial_map|$\pi$-trivial immersions]] of oriented manifolds with prescribed lifts $\widetilde{f}_1:N_1^{n_1} \l
  7 KB (1,269 words) - 13:34, 16 June 2014
• Bonn THDM 2013: Program
  ...ery on an element $x\in \pi_{k+1}(f)$ in the middle dimension if $n=2k$ as immersions may not be regularly homotopic to embeddings. For $k\geqslant 3$ we can do
  17 KB (2,410 words) - 15:27, 29 August 2013
• Embedding (simple definition)
  ...lternative definition]] which works for non-compact manifolds and involves immersions.
  1 KB (184 words) - 07:42, 16 April 2018
• Embeddings in Euclidean space: plan and convention
  [[Immersions: classification]]
  4 KB (571 words) - 00:42, 8 April 2020
• Embeddings of manifolds with boundary: classification
  * analogous results for immersions of manifolds stated in $\S$9, and general position ideas, see e.g. the firs ...a `straightening' of the `immersion' proof because the required results on immersions are proved using handle decomposition.
  34 KB (5,806 words) - 12:26, 21 May 2023